Of course, it is impossible to be sure, but I don't think that he could have evolved too far beyond his genre. Bird lived in a microcosm that he rarely escaped, and when he escaped it, it was usually to a sanitorium (Camarillo State Hospital, for example). This sort of existence does not lend well to development, growth and innovation. Besides, no one would have accepted anything from Bird other than what he did best - this has plagued musicians forever.
I believe that due to his legendary status, jazz would probably have followed his direction to a certain point, but only in an obligatory fashion. It is doubtful that this would have been too far beyond the bebop genre. Jazz would have continued its path of evolution and Bird might have fit in along various intersections of styles and genres, but I don't believe he would have thrived.
Perhaps the answer is in the recordings of Jackie McLean, Sonny Stitt, Phil Woods and other Bird disciples of the time. I don't believe that those guys evolved like Miles or Diz - they went right from bebop to hard bop and not much further beyond. Yes, I know that Phil Woods did some guest studio recordings with Billy Joel and Steely Dan, but those do not reflect his own recordings as a leader, which are in the hard bop style.
One thing is for certain - more modern recording techniques and technology would have improved his sound. I wish Bird could have recorded with Blue Note and Rudy Van Gelder, the greatest jazz recording engineer of all time. Those would have been some amazing recordings!