I was thinking of the plan review of the site/installation. The building itself is just another listed componant isn't it?
You still have to permit the grading, tiedown, utility installation and any other ancillary construction of steps, porches, awnings etc, along with any interior modifications to the trailer.
My wife is in the middle of one of these, setting a sales trailer in a new community. The trailer itself is a listed assembly but the permit process is almost as complicated as if this was site built building. The sales geeks changed the facade and the whole thing had to go back through permitting and plan review.