Yes, with some changes. The cylinders are tipped different on the 05 motor so you have to tweak the y-pipe to make things work.
If you put all the electrics from the 05 on the 01 motor you will have reverse, including the 05 head with the DET sensor. However, the 05 800 timing curve is different than the 01. It will run, just not as much grunt off the bottom end.
You also have to change the carb intake boots to get the airbox to hook up correctly.
Oh, and use the 05 oil pump and pull starter cog.
sled_guy