If there were no punishment for sin would salvation be necessary?
That is a really difficult question, because it references deep theological topics in a fictitious parallel universe, a la C.S. Lewis' Narnia. As the Bible makes clear, sin is punished, and therefore, this question is an irrelevant one (in the practical, real world). However, it is a question that deserves to be answered (have you been reading Plato's Euthyphro, perhaps?) because it uncovers what sin is, and, why salvation is necessary (in that imaginary universe as well as this one). Making a logical inquiry into cause-and-effect relationships is always a good move.
First of all, what is the definition of "punishment"? There is certainly more than one kind. I'll outline them as natural consequences, social incentives, and relational implications.
Natural consequences are the logical consequences of an action, either positive or negative. Normally, when we make our day-to-day decisions about how to live, how to do this-and-that, we mostly take natural consequences into account. Irresponsible behavior can lead to adverse effects on us, such as physical disease/ailment, financial distress, or the risk of injury or premature death. So, as homo sapiens sapiens, most of us (hopefully) can avoid doing things like, say, drunk driving, even without any consideration of the legal, much less spiritual consequences.
Social incentives are the scratch-my-back-I'll-scratch-yours gentlemen's agreements that exist between social beings, and the carrot-and-stick dichotomy set up by an authority figure. Lawbreaking leads to arrest and incarceration, excellence in one's career leads to promotion, negligence leads to termination, etc. The various warnings about the wrath of G-d, fire and brimstone, etc. are a higher-stakes version of this, I suppose. Get back to work, the boss is watching.
This raises a somewhat unsavory question: what if there weren't consequences and incentives? Would sin still be sin? What is sin? And who cares, really? Why shouldn't we sin without restraint?
Paul himself raised this point, Romans 6:1. "What shall we say then? Shall we sin all the more, that grace may abound?"
One of the paradoxes of the Christian faith (or, indeed, any henotheistic/monotheistic faith featuring an authoritative and merciful deity) is that G-d is both demands righteousness and forgives sin. It is difficult to emphasize the forgiveness of G-d (much greater than any human can comprehend, much less practice) without seeming to give people a license to sin. And it is likewise difficult to emphasize the importance of G-d's laws, the severity of sin and its rightful punishment, without making G-d seem vicious and sociopathic, which obviously brings problems of another sort. This balancing act (and other seeming contradictions in the Christian faith) is the reason why there are so many sects in the Christian religion, and so many competing religions (as most of the other big-name religions resemble Christianity or have borrowed from Christianity to an extent). Christianity a great religion, so good that, I believe, people of all other faiths would have converted by now if we had our own house in order.
Back to the Unsavory Question: what is sin? And, without punishment, why should we avoid it?
To understand this question, we need to understand the third form of punishment for sin: relational implications, namely alienation. This is where I start throwing around squishy, liberal-Christian platitudes about separation from G-d. But first, let me hang out a hypothetical:
Would you cheat on your spouse?
Would you cheat if you were sure that you would never get caught? If you knew that you wouldn't lose a bunch of money in a divorce? If you knew that your spouse was inclined to look the other way?
If you knew that there would be no adverse consequences for you personally?
If your spouse finds out, but is willing to tolerate it/unwilling to confront you in any way, that doesn't mean he or she is happy about it. There is still emotional distance, emotional separation. And if your spouse never finds out, well, that emotional distance still exists--but only inside of you. The spouse never knows about it.
You can't bond like you should. You can't share funny anecdotes about how your day went, or take your spouse's phone calls at random times. You can't allow your spouse to speak freely with your friends/acquaintances (what if they say something?). You can't have your spouse planning a surprise date, or night out, as you might have prior commitments and be unable to attend. Even having intimacy would be not-as-enjoyable as it should be, if you're thinking about your paramour and fantasizing about having him/her instead.
And here's the thing: if you feel you're treating yourself to an illicit affair, then you won't know what you're missing at home. It's like the Dunning-Kruger effect. You simply won't know what you don't have with your spouse, that you could have had. You think you're having the best of both worlds. You can say "I love you" to your spouse, who believes you, and it makes you feel good. Being able to say "I love you" feels good. But, unbeknownst to you, being able to say "I love you" and actually mean it feels a lot better.
(none of the above applies to an honest, mutually-supportive open-marriage situation, which I am told exists somewhere)
This brings us to the question of what sin really is. Suppose our good friend Bob is a habitual drunk driver. He never wrecks his car, never injures himself, never gets stopped by a law officer (and therefore, never arrested and never charged with a crime). He never loses his job from it. He thinks he is a good driver. With his good job, good car and lack of criminal record, he thinks he is a respectable and successful member of the American middle class. He isn't bothered. Nobody else is bothered, either. His parents, his siblings, his wife, and grown children, all think, "oh, that's just Bob being Bob. He does that sometimes, it's just his thing."
Is Bob sinning?
Well, how does G-d feel each time Bob does that particular action? Does it fill His Father's Heart with paternal pride? Does it make him pat himself on the back and say, "That's exactly what I made Bob for. Well done." Or does he instead sigh exhaustedly to himself and say, "Well he did it again. I guess I have to love him anyway."
See, it is possible to observe that sin sometimes has no natural consequences. We might even imagine that sinners face no divine recompense, if we play with Scripture enough and invoke the grace and forgiveness of G-d very, very generously. But even under the luckiest circumstances, with the most imaginative (perhaps even hallucinogenic) viewpoint, we cannot hypothesize a world in which sin does not hurt our relationship with G-d (and other meaningful relationships as well). This means that sin is still sin, even in a parallel universe where there is no punishment. There is still punishment... even when there is no punishment.
But I've only proven thus far that "sinning is terrible, even if we are sure that it will go unpunished." I haven't even touched the subject of what it means to be "saved", and why it is necessary.
Too many amateur Christians think that being saved means "not going to hell when you die". That's all it means. First, feel really bad about being born human, then say a five-second prayer (and really really mean it!) and then you won't go to hell when you die, thus sparing the you from enduring the use of torture devices the medieval church used to threaten people with, like in Dante's Inferno.
Jesus' name means "savior". When the angel prophesied of Jesus' birth (Matthew 1), he said, "You shall call his name Jesus, and he shall save his people from their sins." It doesn't say, "He shall save people from hell" or "He shall save people from punishment and torture"; it says "He shall save his people from their sins." My own personal paraphrase says, "And you shall call him 'The Saving I AM', and he's gonna help messed-up people deal with their problems." Why can I get away with saying that? Because that's exactly what he did.
Let's look at an example of what salvation really means (Mark chapter 5): naked dude used to hurt himself and break things; naked dude has awkward conversation with Jesus; naked dude puts some clothes on, stops hurting himself and breaking things. That's a great example of what salvation is, don't you think?
Another example (Luke 19): sleazy bureaucrat steals poor people's money. Sleazy bureaucrat has lunch with Jesus. Sleazy bureaucrat thinks about his life, gives everybody a tax refund. Must have been a pretty good lunch.
In both of these examples stories, there is no mention of either party being threatened with hellfire, or any form of divine punishment. However, both needed to be saved, and both got saved. Saved from themselves.
I think I've said enough; I'll stop now.