Impossible to say.
Though if Richard had seized control of the wave, it would not have ended. He was the last in the line of York, but Henry wasn't the last of the Lancaster. The former making a win at Bosworth would only see him turn the tides temporarily; it would've been a close call that wouldn't instil confidence in the public, and Richard wasn't strong enough to sway them into belief, nor was he enough to make the Lancastrian contenders believe he wasn't to be messed with.
He was always the only thing standing between them and power; he was outnumbered and in way over his head. Fighting them off and desperately attempting to bring the political situation into stability at the same time? No way. So then you have to ask how long could Richard have curbed his inevitable defeat? Henry V fought and won against much more than such a hypothetical scenario. If he had won there, then he wouldn't have spent most of his reign dealing with France because he would be too busy taking up the task of re-stabilizing England. Though really, he could've have done what he did and seen Troyes through since he wouldn't be in the position that caused his premature death, or even the disaster that Thomas caused wouldn't have happened.
In which case, England would have truly conquered France. Anyway, I digress. What I'm really trying to say is that Henry V is a template for a fair king; there were others as, and even more capable; of which Richard would not be able to handle, considering other pressures.