What you are describing here is something akin to rape. (not exactly rape, but similar). So, no the woman would not be responsible for the cost of raising the child.Think of it like this. What if a man somehow stole a woman's eggs and fertilized them with his semen. He then puts the fetus in a piece of machinery that allow it to develop into a fully grown baby. Would you agree that the mother of the baby is still fully responsible for the baby after it's born - that she should be forced to help pay for the costs of raising it?
If you want to describe a scenario where a woman raped a man (yes it is possible) and became pregnant then under those circumstances I would agree that the father does not have responsibility to the child.
Even in my first response to this thread I said there should be an exception in the case of rape. This applies here as well
This raises an interesting question. If there is an incubator somewhere that has the stolen fertilized egg of a woman then I think that woman has the right to "abort" that fetus before it comes to term. Same would apply to an egg fertilized with stolen sperm. We can't steal dna from people and create babies. What a horror scenario that would be. This is one of the reason I initially included 100% safe and effective birth control as one of the conditions. If someone becomes a parent through their own actions then they have some responsibility, if there dna is stolen against their will they don't.