I am sure he will be fine, the noise and vibration of the engine seems to put Mogwi to sleep. We are in the Caribbean just now and he was great on the flight as usual. I have a harness attachment which I attach to him and then to my seat belt so he won't hurt himself if there was some rough turbulence. Most airports have special places where you can let your dog relieve himself after you check in.
When Mogwi was small and not trained yet, I put him in a carrier but he cried a lot so I picked the carrier up and put it on my lap and though I was not allowed to take him out, I opened the door and put as much of my arm in as I could, this calmed him down and he slept.
Good luck
