Any “person” can refuse to pay child support, but int he case of a man, it will eventually catch up with him. It is not necessarily the same with women, which statistically don’t pay far more often than men.
They tend to get out of it, or have it dismissed by a different judge than the one who ordered it. As for men, once they are ordered to pay, they must pay. They can refuse and find ways to make income under the table, but that becomes a life long endevour, since there is no statute of limitations on collecting back child support.
So, whether the woman refuses to kill her child or not is irrelevant to whether she will get a child support order. And once she has the order, she knows that the government will always be on her side to collect it.
Hell, in my years of working with fathers, I’ve seen a case where a woman went after back child support after spending a few years in jail for killing the child. So even if she eventually aborts the child life, she can still get the money owed.