Okay, so not advocating whatever prompted this reply, but as pure thought experiment...No, this is impossible for a completely different reason, for which a woman cannot be her own mother. although in the case of a man, he can become the father of his copy, thus giving rise to another parallel universe. for where did the seed that gave birth to this man originally come from? nothing can come from anywhere, or rather nothing can come from, because it's already there, that is, nothing that isn't anywhere haha =)
Don't try to break the causal link!
UPD: and already pregnant is not a reason because there is super-duper-cool thing known as superfetation or impregnation of womam which is already pregnant =)
If a 20ish yo woman went back in time 20ish years prior, gets knocked up, has kid, leaves kid behind, pops back forward in time...
How is that different from MC going back in time, knocking up Julia with himself, then going back forward in time, implied that he left the kid behind?