Funny, I JUST did this. Went on a trip to the outer banks, which was about 12 hours both ways. On the way there we stopped at the 8 or 9 hour mark to sleep and finished the next day, but on the way back we drove straight through.
I wore my binder the whole way. During the last few hours before we stopped at a hotel on the way up, I was experiencing quite a bit of back pain. I have some chronic conditions that cause pain so I would have been hurting even without a binder, but I'm sure the binder didn't help.
On the way back I slept for 6 hours on and off (yes, I slept in the binder) which made it much easier on me because I didn't have to experience pain the whole way.
In my opinion, if you have a properly fitting binder that allows you to move around and take deep breaths and isn't made of stiff, cheap material, you SHOULD be okay. If your binder isn't too tight and you can truly breathe freely and still stretch your back and such, then wearing it during the ride isn't going to kill you.
Also, all of the naps I've ever taken in my binder were completely accidental. I've always known that it's bad to sleep in your binder, but again, keep in mind that if your binder is truly the right size, falling asleep for a short amount of time isn't going to kill you. If you feel like you might fall asleep and you're worried, maybe ask a buddy to keep an eye on you and wake you up after an hour or so.
The reason I wore it was because I wanted to pass and not have to deal with chest dysphoria. I was also meeting the people that I'd be sharing a vacation house with and I was introducing myself as Luke to them.
