The truck could pull it fine if you could carry it.
I'm thinking the 2" receivers for these trucks have a max tongue weight of around 350#s, so a 400# bike would probably be too heavy. In addition, the hitch mounts on these trucks consist of four nuts welded inside the bottom of the frame rails of the truck. The hitch flanges mount onto the bottom of the truck frame and are held in place with four grade 5 or 8 bolts.
Personally, before I would attempt to carry anything as heavy as your bike, I would want to heavily modify the hitch with some professionally welded heavy metal plate tabs added to the hitch that extend up the side of the outside of the vehicle frame and then attach to the frame with four additional bolts horizontally through the frame in the newly created holes that are sleeved and the side of the frame plated for additional strength as well so the bolts can't tear the frame metal out.
Additionally, I'd also probably opt for some stiffer aftermarket springs (like Old Man Emu springs) to compensate for the significant additional load over your rear axle when you are carrying your bike. Without them, your truck would probably be sagging in the rear significantly.
So could it be done? I suppose anything is possible. But you should also consider your personal liability if your hitch fails and suddenly your bike falls off while cruising down the road... and someone runs into it or it runs over someone. I'll guarantee you the hitch company won't accept any liability for any modifications of their hitch. I don't know if your vehicle insurance would cover your bike repair/replacement either.
It might be better to just purchase a small trailer to tow your bike when you need to. More of a PITA, but probably a safer option in the long run. I do like your idea of the hitch mount though.