Does Sunfire Cape Work when Stealthed as Teemo?

Nope, it doesn't work on stealthed units.

Well, technically it does if you're a regular stealth champion such as Twitch or Evelynn but you'll just end up revealing yourself as soon as you disappear. Teemo would never get stealthed in the first place since Sunfire Cape is always active. (here is confirmation from Riot Eambo talking about Teemo & Twitch's interactions with Sunfire Cape)

If you were to fire up the practice tool, then buy a Sunfire and place an Enemy Dummy in the bush. you can see. Since I've already done that, it takes you out of stealth.