Maybe. There's certainly some kind of mother-bond, as you suggested, but at the same time, how much of it is him actually caring for another and how much is it him being selfish? I mean, it's possible to THINK you're being caring but actually being more selfish than you mean to be. Peter has chivalrous notions but is it because he cares or because he has a sense of honor and what's right and wrong?
Then again, maybe it's enough that he THINKS he's being considerate (seeing how he doesn't know the difference between make believe and reality), or that he has ANY sense of fair play at all (like evening the odds).
Maybe there is something there, although if there is it's certainly stunted, and will remain forever so....