I've seen people with the genny in the back of the truck running. Many have a tanneau cover over the bed and just open the tailgate and run them. I would think that you would want it setting on something that would dampen the vibration of the genny against a metal truck bed. I would think if you didn't that it might be a little louder.
AS far as theft, I would make sure not to leave it out in view while you are there. If you can put it in the back of the truck and cover it somehow, that would be good. If you have a locking bed cover, even better.