Yes you will feel the coach moving on the suspension when someone is moving around in the coach. The mover won't feel it but everyone else will. You can level with various methods under the wheels but without something directly supporting the chassis frame to the ground the coach will bounce on the suspension.
I'm the second owner of my coach which came from the factory without jacks, levelers or other type of stabilization hardware. First two years of ownership if I was parked for more than three nights I would use 12 ton jack stands and a matching bottle jack to level and stabilize the coach. Have since add a four point hydraulic system.