I would agree you can answer "no".

Most employers don't have access to the FBI database, airlines do for national security reasons. This means they might have visibility on non-conviction arrests which would otherwise be hard to find out about.

Not sure if all misdemeanors make the FBI list, I think it's generally for felonies, but maybe things like DUI too.

If DAL does the background check BEFORE offering you a job, it's possible they might see it and decide not to extend the job offer. Probably not legal, but nobody would know other than a few ATL good ol boys. But if you're already in class when they run the background check, I don't think they could practically fire you...

1) You didn't lie
2) They aren't really supposed to use the FBI info for generic employment screening, it's really more for security.

So while they would probably WANT to fire you, they would have to be willing to fight and lose the lawsuit. It would also depend on what the actual charge was, how long ago, and your age at the time...

Urinating in public at age 15, they'd probably let it slide.

Desecrating a corpse at age 35, they would rather pay out the lawsuit.

I suppose another risk might be that they could arrange for you to fail out of training. This was common in the past if airlines hired somebody and then decided they didn't like them for whatever reason, they would make sure they never got off probation. They would have "designated hitter" examiners who were in tight with management for this purpose. But that sort of thing is much harder today with modern employment laws and scripted AQP crew training. Probably nothing to worry about at the big three.