You're technically breaking the law in pretty much every state, but the consequences vary wildly depending on where you are. Some places treat it as a minor fix-it ticket that you can usually dismiss once you get the inspection done, while others slap you with a proper traffic violation that goes on your record. A cop can absolutely pull you over for it, and whether they actually do depends on how vigilant local enforcement is in your area.
The real issue is that you're not just risking a fine - driving with an expired sticker can complicate things if you get pulled over for something else or end up in an accident. Insurance companies sometimes use it as an excuse to deny claims or raise your rates. I had a friend who got stopped for a burned-out taillight and ended up with both a violation for that plus a separate ticket for the expired inspection, so it can stack up quick.
Just bite the bullet and get it done. Most inspections don't take more than an hour at any shop, and it'll save you way more headache than the minor inconvenience of scheduling an appointment. Depending on your state, you might even be able to get a quick pre-inspection check online before you go in if you're worried about failing.