Like everyone has said it's complicated because you're going to have to do some legwork to figure out the laws in each state (and sometimes municipalities) you're traveling through. You also have to be mindful of not only your company's policy but also those of the places you're loading and unloading at.
The good news is 29 States now have Constitutional Carry and if you have a state issued permit reciprocity with other States can open up more places you're allowed to conceal carry. You have to make judgement call for everywhere else, weigh the risks vs rewards. FOPA covers you as long as you are following the transportation rules as far as storage but beware some States don't allow stops or only "reasonable" short stops in State under FOPA and some like New York, New Jersey shit all over the FOPA without repercussions.