Of course. Our daughter hunt/jumps a race-bred/Skipper W horse and wins lots onboard. We presently have a double bred Doc Bar colt being shown in Pennsylvania as a dressage/jumper. Go for it. Welcome to the quarter horse breed.
jumpe with a couple of quarter horses when they were in fashion here in europe. crappy lower legwork. they can't stand jumping more then 1.20m for more then one competition season. after that their pipes get swollen and their joints get ruined.
if it's just for fun, not heavy competition, go for it, because they are fun horses, but their legs are a pain in the ass for competion jumping (1.40 to 1.60m)