No he won't, because he can't even if he wants to. Overturning Roe sent the issue back to the states, it is no longer a Federal matter. This is fear porn for the Left base.
Your comment reads like "Don't threaten me with the supreme court!" in 2016. Overturning Roe was fear porn for the Left too, but the Right was crazy enough to actually do it. It's incredibly foolish to write this off, only for the next Republican administration to ban it.
If precedent mattered, then Barrett wouldn't have been considered by the Senate, since they had just established in 2016 that you can't confirm a judge in an election year. The hypocrisy clearly isn't a disqualifier in Barrett's eyes. Alito thinks the Court is quite literally above the law. And Thomas has a sweet gig where he's getting loads of free shit and vacations in return for being as conservative as possible.
Don't assume that the Court will be consistent, especially since they were already inconsistent by overturning Roe. They'd already blowing up in their face, and I say we should toss barrels of gasoline on that fire. We need a heavily blue Congress to remind Alito that he is a servant, not a king.