I think with most potential employers (airline and others) you can specify that they are NOT to contact your current employer. Although they will ultimately have to do so for PRIA if no other reason, that can be deferred until you are offered a job or better yet start class.

I've never heard of an airline firing a probie for applying elsewhere, and I'm not even sure that would be legal in all states. But you're probably wise to tread lightly.