Don't know if he would have been successful. That was the era of Rainey, Swantz and then Doohan. And Doohan was like a metronome when it came to his racing. The legend of the era (and yes other eras had their own legends).
Personally, up against those guys, don't think he would stack up
MotoGP is actually the era after this. It began in 2002. Rainey and Schwantz both quit racing GP, due to injuries back in the mid 90s. Mad Mick quit racing after 1999 (again probably due to years worth of injuries - his right leg was basically permanently trashed from a crash on the track), and IMO, he was one of the reasons why MotoGP came about. Him winning several years in a row, being a phenomenal rider, and riding one of the Big 4 machines (Honda), that had a lot of expensive R&D put into it (that most other teams couldn't afford), and on another "same old same old" 4 cylinder 500cc bike (in 1968, the FIM, drastically restricted the engine types that could be used in GP motorcycles - no more wacky 6 cylinder 500s or 250s. no more 5 cylinder 125cc bikes with 8 speed transmissions that revved to 20,000 plus rpm, etc.), brought about the MotoGP rules that allowed some engine variety (at least for a few years - lately IMO, it's become like Superbike on steroids, due to engine restrictions existing again), and the shaking up of things competition-wise (neither Aprilia, nor Ducati [with the exception of a short period on the late 80s or early 90s] competed in the old [premier] 500cc class, whereas they both compete in MotoGP).
As for Michael Schmacher - if he was as good a rider as he was a driver, yeah, he could have made some waves in MotoGP, but while crossover rider/drivers have done well, they have seemed to be better at one (riding or driving) than the other. Also, IMO Formula 1 is by far more popular than MotoGP (as much as I hate to admit it, since I'm a motorcycle rider), so if Schumacher was top dog in MotoGP, instead of Formula 1, he wouldn't be as well known.