Does it not depend on how much you are swapping over?
If you put a 2001 engine in a 1997 car, if you use all the 1997 ancillaries such as starter, alternator, intake and exhaust manifolds etc. do you not remove a lot of the obstacles?
I'd doubt you would have to change the ecu and loom if you did this.
Another thing. The 2.0 156 engine has twin balancer shafts and another belt hidden in behind the cam belt cover, I haven't looked to see if there's space but you'd need an extra inch or so clearance in the Barchetta bay for it to go in.