Possible? Yes.
Simple swap? No.
You will need at the very least: 4v heads/cams/intake/valve covers, 4v throttle body, 4v exhaust manifold, 4v timing cover, 4v wire harness, and probaly a few other odds and ends I am forgetting.
All in all, it gets pretty in depth and isn't a "simple" swap.
My reccomendation is doing a PI (Power Improved, all 99-04 Mustang heads are PI) heads/cam/intake swap. Using stock parts (which can be had MUCH cheaper than the average 4v setup) will give you even a little more boost over what a stock 99-04 4.6 would make because when you put PI heads on a non-PI shortblock it bumps the compression ratio a bit due to the design of the pistons on the 96-98 engines.
With full bolt ons and stock PI cams I imagine you could see 270 rwhp with a decent tune. Add cams into the mix and watch the numbers get closer to where you want them to. Not satisfied? Have the heads ported before they go on, and put some more agressive cams in them. I would be shocked if you didn't see over 300rwhp like that.
Obviously as you do more and more it adds up, but I would almost garantee you a PI 2v swap, or 2v PI swap + cams will satisfy you.