Nah, in the few enforcement actions I've read, they nail down the case by capturing transmissions with the fancy monitoring van's gear so they can "fingerprint" the transmitter. (Ramp up time, audio clicks and button press audio, etc... All make each transmitter pretty easy to ID... Think of it like ballistics study of a firearm used in a crime.)
For a license that costs $200/10 years... Or $20 a year... They're so understaffed they're not rolling a truck unless you're interfering with another properly licensed station, or some turd is making the Field Office's life hell by calling every day and writing letters.
In the OP's case, there's a "suspected turd" involved, so the simple fix is $200 to forget about renewing it again in 10 years.
Again, I have other FCC licenses at risk so I'd comply with the license requirement. CFIs and others with little to lose, may not care...
I had someone "bootlegging" one of my callsigns once. I had a couple of recorded chats with a Denver Field Office Agent after a VERY connected person complained (probably to a Commissioner or high-level Engineer) about the interference.
I had an airtight alibi and also didn't own any gear appropriate for the frequency. The chat was really to built a docket against the true interference source, which I learned had been easily triangulated to a location about 45 miles northwest of my home. I was President of an Amateur Radio club at the time, and was an "easy" target for the trash who wanted to cause trouble, I guess.
RF Direction Finding is not difficult for the FCC anymore. It's automated, in fact. Don't transmit, you're good. They're busy filtering through "hits" on the automated systems.
I've also been the person on the other side of this complaint, and indirectly involved in a lawsuit by someone who was operating illegally through someone else's "Repeater" station. That one got as far as a warning letter from the FCC counsel.
Both of those situations took YEARS to play out. They really don't have the time.