The short answer would by yes. Fit is not an issue, that part would be easy. However several other things would need to be changed. Wiring harnesses, computer modules, I doubt the Allison would need to be changed out. Most likely just updated. With it being an 01, I'd guess that you'd have to change quite a bit more than you would an 03 or 04. You'd have to update the truck first. I don't think this would be very hard, just expensive and time consuming. It's the equivalent of upgrading the LT1 to an LS1 in a camaro. Again, very possible, but for how much...
I'd just go for a truck with one already in it. When your truck has seen enough miles to kill the LB7, there will hopefully be used LLYs out there. Then buying a used one with an LLY in it would be much simpler and less expensive.
Ox