Not exactly, but you can kind of do it with tonematching. I have a guitar that I put nice new pickups in a while back, and recently I was remixing some old recordings I'd done with the old pickups in the guitar. I had recorded with with my Axe, and had the foresight to record the dry track for reamping, so I took the try track of the recording with the old pickups, tonematched it to my guitar currently with the new pickups, and then reamped the tonematched dry signal back through the Axe (with much newer and better sounding firmware). The result was pretty good. The mutated old recordings sounded very similar to the tone of my guitar with the current new pickups when played through the same patch on my Axe. It's not 100%, but it was pretty close, and was very musical and useable none the less.
Now that said, that was all using exactly the same guitar. I don't know how much success you'd have making a Les Paul sound like a Strat, though.