No, it's pretty unlikely that while a probation travel restriction that anyone at the airport would flag you if you tried to take a trip. The airlines do check ID as part of homeland security requirements, but they are not matching that to probation databases. The only exception I can think of is if you have a warrant issued for your arrest and you fly internationally and fly back into the country and have to check in thought customs. In that situation, the Customs people will probably find the warrant and arrest you.
By the way, why are you traveling against your probation restrictions? Most probation systems allow you to ask for a trip permit and you cannot be denied unless there is some good cause. Violation of travel restrictions, if you get caught, could land you back in jail, so think wisely before you decide to break your probation.