I'm sure it depends on the dog.
For example, with me, if it were Jada, she would just lay back there the entire ride, calm and cool. However, Riley would jump all over the place and probably hurt himself He's a little bit of a spazz!!!

About the four legs thing, I had never thought about it that way, but I think you're right. Kito stands in my CRV all the time and never falls over--he even tilts with the bends to keep his balance.