How would the FAA catch people without licenses?
If they are conducting a ramp check and you don’t have a license, the chances of getting caught are 100%.  The size of the airport, the presence of a control tower, or the surface of the runway is immaterial - if it is a public airport the FAA could be there.
If they are not conducting ramp checks, you would only be caught if there were a reportable incident that brings your activity to their attention.  (airspace violation, noise complaint or tip, mishap, etc.) Otherwise, how would they know?
I’m not sure how it might work at a private airport, but I would imagine the FAA would be held to the same standards as law enforcement; i.e. they would require either consent, probable cause, or a warrant to enter your property.