I have personally seen Humvee's driving on the roads so I dont see why not.
Basically an MRAP is just a big truck so as long as it didn't break any traffic laws (too wide, too heavy, etc) then I'd assume its fine. Would depend per state though.
Anecdote from 6 months ago: Humvees are often sold without title for $4K to $8K in GA. Titled vehicles (the ones that can legally drive on public roads) go for $22k for a beater on up.