While we will never know, as in all "time machine" fights, I would have liked Joe's chances. Joe fought during one of the strongest heavyweight eras; Tyson during one of the weakest. Tyson was a frontrunner who relied heavily on intimidation; many of his opponents were scared shitless before the fight even started (Bruce Seldon even went down from a "punch" that video showed didn't even land.) On the occasions when his opponents didn't fall apart, Tyson did. I'm mainly thinking Douglas and Holyfield. When a few wild haymakers in the early rounds failed to close the show, Tyson had no Plan B.
I don't know if Tyson could have hung with a guy who could fight him on more or less even terms on the inside. Remember, Foreman had a big size advantage, both height and reach, over Frazier that Tyson would not have had. My guess, based on watching both their careers and taking into account the caliber of their opposition, is that if anybody would crumble in that scenario, it wouldn't be Frazier. Put another way, it would have come down to whether Tyson was too much fighter for Frazier, or Frazier was too much man for Tyson. My money would be on the latter.
Anyway, blessings to the great Smokin' Joe.