The question posed in the OP is that Roe v Wade is overturned. I think we have to be clear that, contrary to some demagogic remarks, courts do not legislate. What they do is decide individual cases as they come before them, and in so doing, set precedent which other courts may, and in some cases are obliged to, follow, in dealing with similar cases.
So the question then becomes, what are the circumstances in which Roe v Wade is overturned? And the answer to the hypothetical must deal directly with that situation.
While I can have a great deal of sympathy for the proposition that an unborn fetus is a person with rights, the Constitution does not deal with the question of what “persons” have rights, but rather with the rights of citizens of the United States. To a lesser extent, it has been interpreted to deal with what rights legally recognized persons who are not citizens may have – legally resident aliens, corporations in their capacity as legal persons, etc. But its focus as regards rights are on those possessed by citizens.
That may be important to keep in mind, given the Amendment XIV definition of citizen.
Now, the principal effect of Roe v Wade was in suggesting that a woman has a right to privacy over her own body and what shall be done with it, which a state may not supersede by mandating that she not terminate a pregnancy. (Let’s note that an abortion is a medical or surgical procedure that has the effect of terminating a pregnancy – women have, for example, D&C’s all the time when not pregnant, for medically appropriate reasons; a D&C on a pregnant woman becomes an abortion. So technically there is no “right to have an abortion” – what there is, is a prohibition on a state’s regulating a right to teminate a pregnancy. Semantics, but I think important ones, given the circumstances.
Also, Roe v Wade did not bar the prohibition of abortions generally; it merely specified that there were times and circumstances when states could not impede the woman’s right to terminate her pregnancy.
So the question of what the specifics of the case in which the overturning of RvW are, and how the decision is written, becomes paramount.
It’s very easy to write headnotes that say “Prohibits states from banning abortions” – but that’s not what the decision says; that’s not how it was generated; and that’s not what the issue reversing it may be.
I personally think that Mr. Blackmun engaged in some of the sloppiest legal writing on record in that decision, producing the bastard child of a Brandeis brief and a J.A.M.A. case history rather than a Supreme Court decision – but that is neither here nor there.
Justice O’Connor’s stance on issues regarding abortion generally may be of particular interest in analyzing what might be the outcome of such a case.