Yep, it's possible, but AuH2ORepublican is probably right that Bork would have retired during Bush's second term rather than risk a RAT winning the Presidency in 2008. He was 60 at the time of his nomination, one of the reasons we need to nominate younger judges. Few would anticipate a 60 year old staying on the court for 25 years, though it seems routine for Senators to stick around that long.
It would be interesting to go back and look at all the 5-4 decisions over the last 25 years where Justice Kennedy sided with the liberals, because nearly all of them would have gone the other way. This would be a very different country today. As others noted, Roe v. Wade might have been overturned in the Casey decision of 1992. (I think that ruling might have been 6-3 though).
Bork did accurately predict we were "Slouching towards Gomorrah" in 1996. Sorry, George W. Bush. Even your veep jumped on the bandwagon, at least on the gay marriage thing.
Gerald Ford actually considered Bork for a SCOTUS seat in the 70s, but concluded (accurately, unfortunately) that he was "too controversial" because of his role in Richard Nixon's firing of Watergate Special Prosecutor, and the Dems would destroy him. So Ford crossed him off the short list and we eventually ended with the horrid John Paul Stevens.
Incidentally, Specter and five other RINOs joined the Dems in opposing Bork. Yet we're always told we "have to" elect RINO Senators so we can get good judges on the courts. Poo.
Casey was 6-3 (Kennedy and O’Connor both switched to support Roe’s ridiculous holding), but once Thomas replaced Marshall the Court had 4 strong votes to overturn Roe, and had Bork been there instead of Kennedy then there would have been 5 solid votes to overturn. (Of course, a couple of years later White was replaced with Ginsburg, but by that time Roe would no longer be a binding precedent and O’Connor could cite stare decisis to uphold the precedent stating that states could ban abortion.)