I think it depends on your definition of good. Different people define good in different ways. Until good is defined clearly, it's impossible to answer this question with clarity.
From the Christian perspective:
All good comes from God (James 1:17)
Every good gift and every perfect gift is from above, coming down from
the Father of lights with whom there is no variation or shadow due to
The Christian also believes that it is chiefly our motivations that will be judged. Jesus was frustrated with the motives of the scribes and Pharisees, who did all the right things for all the wrong reasons (Matthew 23:27):
Woe to you, scribes and Pharisees, hypocrites! For you are like
whitewashed tombs, which outwardly appear beautiful, but within are
full of dead people's bones and all uncleanness.
Also, Paul reinforces this point regarding the importance of our motives (1 Corinthians 4:5):
Therefore do not pronounce judgment before the time, before the Lord
comes, who will bring to light the things now hidden in darkness and
will disclose the purposes of the heart. Then each one will receive
his commendation from God.
So what is good according to the Bible? Jesus says this: (Matthew 22:36-40):
“Teacher, which is the great commandment in the Law?” And he said to
him, “You shall love the Lord your God with all your heart and with
all your soul and with all your mind. This is the great and first
commandment. And a second is like it: You shall love your neighbor as
yourself. On these two commandments depend all the Law and the
So why do we love, ultimately? (1 John 4:19)
We love because he first loved us.
The Bible's definition of good thus consists of:
- What we do.
- Why we do it.
- Who defines it.
So in a nutshell, if God goes bye-bye, we lose not only the commandments of God, but we also lose the ability to have the proper motivation for it, and we also lose the Chief Determiner of Good Himself.
At that point, "good" simply disappears. It's not that we can or can't do good. It's that good ceases to be good, and begins being something else.
Of course, if you define good by what the general populus, or what certain individuals define as good, then of course, everybody could do good. But more than likely, everyone's definition of good will differ, so one person's good will be another person's evil.
The Bible talks about this as well (Judges 21:25):
In those days there was no king in Israel. Everyone did what was right
in his own eyes.
Without God, it's impossible to define good, at least in a Biblical sense. So in order to answer the question, good would need to be redefined.