Yes. Our cat has free roam of the trailer while traveling. She hunkers down in her bed, but will meet us at the back door every time we stop. Her bed is on the floor between the wall and bed. Even when we had our "Loose Wheels*" accident, she was fine. We also put her in the night before we leave...in this way she gets accustomed to being in there, then next day there is no meowing.
She has traveled all across N. America and Canada this way. She always wears a harness in campgrounds.
(* Do a search if you wish to read this.)