Depends on what you mean by jumping him.
If you want to lark over logs and crossrails when you pleasure ride, or jump courses of 2' to 3' he should be fine. If your ambition is rated hunters, jumpers at 3'6" and above, or eventing at Training Level and above, I don't think he's the right horse for the job.
I'd be careful to make sure he was very fit before starting over fences, and keep the fences fairly low; as his long back and flat loin and croup predisposes him to "jumper's bump."
Don't mean to be a smart alec here; but the sports STBs are best suited for are ones that involve pulling a carraige or doing lots of trotting.
Since they are generally sweet-natured and willing souls, you can train them to do just about anything, but pulling and driving is what they were bred to do.
If he were mine, I'd either get a harness and carriage and drive him, or do some long distance trail riding where that ability to stay in a long, steady trot would an advantage.