We have done something similar to what you suggest without problems. While on vacation at a Land Between the Lakes campground, on a hot sticky night, I decided to try running our EU6500is Honda all night to supply power to our Keystone Premier 22RBPR. We have a Dodge 1500 truck with a cap/camper on the bed. We were unhitched, so I had the tail gate down and the two side windows open on the truck camper (I don't recall if I ran a fan to help exhaust the fumes or not, that is a good idea). I had the genny secured to the steel loops in the bed of the truck to deter theft.
It worked great. I don't see how fumes in the truck cab would be an issue, since you would not be in the truck cab anyway and, assuming fumes migrated into the truck cab, it would presumably dissipate readily by opening the truck doors.
If you can't open the tailgate all the way, I would leave the truck cap/camper door open and I would run a fan to aid in exhausting the fumes from the truck cap and to keep the space cooler.
Joe