Possibly. He would have needed to have done the following:
1. He needed to have picked a Southern running mate from a state he was not sure to lose. Sam Nunn of Georgia, Ernest Hollings of South Carolina, even Richard Shelby of Alabama would have been better picks than Bentsen (who, admittedly, would have defeated Bush head to head in Texas).
The problem is he needs a running-mate that's conservative but not
too conservative. Hollings and Shelby aren't it. Nunn might be grudgingly accepted, but he would likely be viewed as more "presidential" than Dukakis, thus the same problem that he had with Bentsen. Dukakis at least picks up Georgia, however, as Nunn was way more popular with Georgians than Bentsen with Texans.