I suppose this is increasingly a possibility. You're thinking of the Highwayman, which was a faster way of getting around the overland map in Fo2, and can be seen wrecked in a muck pit in New Vegas.
If you're thinking Road Warrior, that seems unlikely. it's been established that most vehicles have stopped working, and those that do are treasured artifacts created by governments or high tech factions. I can't really see stuff like that spilling into the general populace enough to have Biker Gangs. furthermore, no gasoline means none of the weird darwinism of the Road Warrior.
Still, some kind of car or motercycle stuff might be cool, provided it's done carefully and not slapped onto the top of it. they need to balance such things between "NPC's will blithely ignore you as you land a twenty foot jump on their face" and "Unstopable juggernaut you might as well never get out of for how thoroughly it wrecks raiders."
The key would likely be a mixture of the cars taking damage and needing some kind of fuel. The Highwayman ran on energy cells, so that's a possibility, but couldn't be used in combat, so damage wasn't part of its nature.
so long as the controls, context, and physics are considered carefully, I think it could work fine.