When you do that you're supposed to classify the vehicle as an OHV, or off-highway vehicle. Problem is a lot of states don't actually do emissions testing, others don't do vehicle status inspection, and some don't do either. You ever wonder why Indiana has such a huge number of drag racing cars in the Prostock and Superstock classes? There's no emissions testing outside the capitol.
Having grown up in Indiana, and having watched a lot of drag racing, and even crewed for a friend drag racing motorcycles, I have not once wondered that, either. I, of course, just assumed it was that way everywhere. “What, your small nowhere town doesn’t have its own drag strip or dirt oval? How odd…”
(And when I say “nowhere”, I mean go look up Bunker Hill, IN as a go-to example. It’s a fine town as far as small towns go, but a long way from any major metro.)
Back when people still watched cable Street Outlaws was Discovery's biggest show for a while. It is an oddly specific thing, but a question I heard a lot about ten years ago. The two places where drag racing are biggest are Oklahoma and Indiana.
Of course, the emissions testing is a state issue. Even the federal regulations say that federal government vehicles have to be tested in the state they are stationed in.