He was to narcissistic to remain hidden. He probably would have surfaced in Europe with in a couple of years.
I don't know if there were extradition treaties at that time.
There actually was someone claiming that Booth did NOT die in 1865 but escaped for many decades,lived incognito then fessed his 'real ID' on his deathbed . However; person was a sideshow carnie who displayed the purported Booth's mummy for some years so this is something that likely needs to be taken with a mine of salt.
unless you want to believe he would somehow lead some major group in some sort of uprising/distraction, there'd be no real difference. Lincoln is still dead, and the rest of the plan went wrong. Booth being alive but laying low doesn't change a thing. If he doesn't lay low, he gets caught and killed.