The only way to play him is if you use all of your cooldowns clearing every camp every time they're up, otherwise you'll be pretty slow. Since you're constantly spamming skills, you run out of mana extremely fast and can't gank well either. Best played in a lane.
A lot of junglers can work if they do "okay". If they enable a couple ganks and fail a couple ones, and lose a couple buffs too many to the enemy jungler, but take dragon, they'll still be able to contribute overall. Maybe enough damage to take out a squishy before a bruiser crushes them, maybe they can initiate well, maybe they got some CC.
Jayce is not one of these junglers. Jayce needs to be effing amazing to get anything done without lane income. If he only does "okay" then he's basically got nothing.
Of course if you are effing amazing and do everything right then he's a scary-ass force of nature. So, you know, high-risk, high-reward, that sort of thing. But I wouldn't recommend it. There are way safer picks out there that will work at least as well if you play them perfectly. --- "ˇViva La Revolución!" -Salvador Limones