Supercharging a WRX engine totally does work!

^I know this isn't actually relevant, but I still thought it was worth sharing.

Phil and Cdn both nailed it. The only point I could add is that of the few people supercharging WRX engines, the goal is normally to combat turbo lag, so they are used in a twincharged application (like the article above). I've seen numerous supercharged NA Subarus and a few twincharged WRX engines, but can't recall ever seeing a turbo-supercharger conversion.

If heat is your concern, I third the idea of AWIC. We have an 818S with an AWIC and no extra rear ventilation, and have no heat issues (At least, not with outside temperatures in the 80's).