Don't know about Chicago Express, but at ATA, officially, the short answer is yes. However, the final authority rests with the Captain. If you're with some operator that he hasn't heard of, he may be leary of letting you on. If you do attempt it, be prepared for some questions about your company, and the equipment you fly. Come with all your certificates and an official picture ID (passport, drivers license) along with your company ID. I'd also be in full uniform. You may need to pick up a jumpseat form at the ticket counter if you can't get to the gate. (See suggestion above about wearing full uniform). Otherwise, you can request a form at the gate.
Good luck.