Not really. The reason the overturning of Roe was widely considered to be inevitable, even by jurists who were pro-choice, is that the theory of privacy used in that case was fundamentally incompatible with a broad range of regulatory powers most people think the Constitution grants the Federal government.
The reasoning behind Roe was generally regarded as tenuous even by the justices that supported it. Overturning it was required to defend the government’s Constitutional authority for agencies like the FDA, which was undermined by inconsistencies introduced by Roe v Wade. Eventually those judicial inconsistencies come home to roost.
tl;dr: Roe being overturned had little to do with privacy and more to do with protecting specific regulatory powers from being unconstitutional using the same reasoning introduced in Roe v Wade.
Removing such decisions from Federal purview was an elegant solution to the problem, with the practical effect of deferring all such decisions to voters at the State level.