Eagle is the most likely of the regionals to be anal about something like this, but given that they are offering $5K signing bonuses, who knows.
In order to obtain info on lesser (non-DUI) vehicle infractions, employers generally need to go to the state in question. Even if they went to every state you've lived in/held a license in, they still might miss a ticket that you got in another state. Also not all states seem to keep good records going back very far. An employer might also hire an applicant screening service to do the digging although there are legal limitations on that.
Basically it's a crap shoot. If you can't find it, odds are reasonable that they won't either. But the stakes are very high...
They usually don't spend the time and money on extensive background checks until AFTER you show up for class...if they find something you didn't report (usually about two weeks into ground school), you'll be pulled out of class, given an opportunity to dispute what they found, and then terminated. You now have no job, but have been employed by a 121 carrier, and fired for lying. You have a very short, and very ugly PRIA record. Your brief, brilliant, airline career is most likely over for good.
Any typical new-hire class at any regional has one these occurrences, especially a large class. There's always some noob who thinks they won't bother, won't find out, or won't care. He's wrong.
Conventional wisdom is don't lie, but only you can make the call. How comfortable are you having it hanging over your head.