Somehow they just seem to find out...almost every airline new-hire class has one guy who gets pulled out of class in the middle of the day around week 2-3 and is never heard from again.

How would explain the gap in employment? You are always required to document what/where you were doing...work, school, or unemployed. They pay close attention to unemployment periods, they know how long it usually takes to bust out of training...you would not be the first to try this.

What happens when they call the employer you had before PSA? You sure they won't mention that you left for PSA? The airline will be particularly inquisitive since you resigned from that employer only to be become "unemployed"...they will suspect you were fired from THAT job and will naturally wonder why.

Also PSA probably ran a TSA background check on you...I don't know for sure, but knowing the government I suspect they keep records of that.