I'll take a stab - initially it should be possible, they both used the Essex 3.8 V6. The Cougar used a different trans though, and I'm not sure if the wiring harness would work as the cougar had a lot of additional stuff your Mustang doesn't (electronically adjustable suspension, etc). So at first blush it looks maybe do-able with some potential obstacles.
The more important question, I think, is why that particular engine. It was supercharged in the Cougar, and the only real difference between engines that I am aware of is lower compression ratio in the supercharged version. Is that why you want to turbo it - because it already has lower compression?
Edit: just saw your post update - the Cougar engine should already be supercharged. Having said that, if you are interested in supercharging, there are several folks here that have supercharged a V6, Orange 94 being one of them - he will probably have better advice for you if that's the route you want to take.