It really depends on the Thorughbred, but if you and the horse are capable, it's entirely possible. Historically, showjumping was dominated by thoughbreds, many of who were OTTB's. If you do some poking around on the internet, there were OTTBs in the Olympics before the warmblood fad came around. Hope that helps!
I have had several that I've trained from the track up to that point, but sold before they ended up with a USEF record. Had one I brought up off the track who was supposed to be my 1.40m+ horse but some freak stuff killed hay dream before she was able to to prove herself. Was schooling 1.30m courses and up to 1.50m singles