Even from a Christian perspective, I would say that, in a sense, they can do good without God. Of course, according to Christian belief all good things come from God (John 3:27; James 1:17; Tob. 4:19), but what I mean is, they can do good through God while not realising it, and while lacking faith in God. I think Paul hints at this when he says:
"For as many as have sinned without law shall also perish without law: and as many as have sinned in the law shall be judged by the law; (For not the hearers of the law are just before God, but the doers of the law shall be justified. For when the Gentiles, which have not the law, do by nature the things contained in the law, these, having not the law, are a law unto themselves: Which shew the work of the law written in their hearts, their conscience also bearing witness, and their thoughts the mean while accusing or else excusing one another;)" - Rom. 2:12-15
So if people, inclined towards the good by God's nudging (Phil. 2:13), are doing that "law written in their hearts," they can still be said to be doing good, even if they don't know that it's God behind it.