The cobra motor will fit just fine. It is pretty much the exact same block but w/ forged internals.
The question is when your are talking motor are you talking shortblock or a fully dressed block? A 4v head motor in your GT's engine compartment will require some minor modifications.
if you'd search around, you would find a bunch of threads on this swap. But yes, it will fit. You'll need the cobra's wiring harness though, among many other things.
As a 2V owner you do have some options. Check out the Torktec (sp?) kits. You do one of those and some Trick Flow heads and I'd wager you can make some pretty serious power.
There is a lot involved with a terminator swap. You need the ECU from an 03-04 Cobra, the cluster, and the engine would need to be complete w/ all necessary sensors. Would you also be using the T-56 trans?
Is there any reason you don't want to build up the 2V?
If you can get the Cobra motor I would say do it. As long as you get the complete harness and ECU the wiring should be plug and play. As long as you plan on taking your time the it shouldn't be overly complicated.
Someone mentioned the Tork Tech kit earlier and I did that to my 01 GT and love it. I'm only running 7psi of boost and putting down 378 HP. There is plenty more left in my setup if I were to swap a smaller pulley, but as it is now I can't even launch hard in 1st gear. Once I have the tires catch and brakes catch up I might go for more power.