Some kids feel the pull-up or diaper and their brains and bodies tell them that the feel means it's OK to "go" when they like. The idea of putting on a pull-up over the underwear is more for your convenience for clean-up than to teach him anything about pottying. I would put a plastic liner (the kind you use for diaper changes, with one absorbent side and one plastic-coated side) in the car seat beneath him, and have wipes and extra clothes right there on the seat next to him, and scope out all the rest stop and restaurant bathrooms between your house and Savannah. It's only one hour. He's learning to potty. To me, the pull-up plus underwear would seem to send a confusing mixed message to a child who's learning to use the toilet.
You also can carry a portable potty in the car. We used to have a station wagon when my daughter was small and she could get on the potty in back of it if we stopped for a potty break and used it then and there. You can do the same in a minivan, I'm sure; not sure how it would work in a regular car but to be frank, you can put a plastic sheet over a seat and put the potty on it if you must! You line the inside bowl of the potty with a couple of plastic bags to catch the urine and poop, then throw it away when he's done (and yes, if it's the middle of nowhere, you tie it up and put it in another bag until you get to a bathroom). Or put a clean, opened diaper into the potty if he's only peeing and dispose of that later.
It's much more hassle than putting a pull-up on over his underwear so I can see using the pull-up; it just depends on how you feel about consistency with having him use a potty or toilet every single time. It won't destroy his potty training if you do the pull-up, I'm sure.