I'm going to start with some base assumptions, because I sense that the atheists are going to have a field day with this, and I'm hoping to prevent this from turning into a debate on whether or not God exists, is good, etc. The assumptions are those that are necessary for this site. IMO, the debate over the assumptions on which this site are off-topic. Those debates have nothing to do with the question asked
Assuming that God is who the Bible claims He is (a core assumption of Christianity), then He is all-knowing...
Assuming again, that the Bible is God's word, given to us by His divine inspiration, and preserved through time (again, a core assumption of Christianity)...
And further assuming that God loves us, and is good, and knows what's best for us...
Then yes, Biblical advice can absolutely help an unbeliever. In addition to pointing to God, and Christ as savior, the Bible is chock full of wisdom that is applicable to daily life. If God loves us (as the Bible says He does), then He will give us good advice, and instructions that are for our own good. His wisdom is good, regardless of whether not an individual believes it.
The instructions on how husbands and wives are supposed to love and respect each other in Ephesians 5, for example, will strengthen the relationship of anyone who chooses to follow them, regardless of whether they are Christian or not. Similarly, advice to love our neighbors (and our enemies) as we love ourselves will benefit anyone. Most strife in relationships is caused by selfishness on one or both parts. Two completely selfless people, devoted to loving each other as God intended would have nothing to fight about. (Of course, there is no such thing as a completely selfless human being.)
The question is whether or not they will choose to follow Biblical advice and apply it. Plenty of people will reject even the best advice, if it comes from a source they don't agree with.