Of course they can. Thats the 'C" in conditional.
Will they be? it's pretty unusual. unless there's something you've not been honest about. Chances are they'll find out. Every airline will look into your background; generally with a third party screening company. There's not a lot of things that are disqualifying. Except trying to hide something. I've seen people pulled out of class and sent home for being untruthful.
If you feel there's something in your past that may be unsavory; discuss it with HR. They'll generally work with you.
//PL