The helicopters have to be flown anyhow, if for no other reason than to keep the pilot's air hours current.
You are constantly flying Blackhawks along the Canadian border too. They are supposed to prevent grain and beef smugglers from driving over the border across the empty wheat fields.

These helicopters are extremely well equipped for locating any warm bodies.
The cost of diverting one from the patrolling the Alberta/Montana border (as an example) for a day is pretty minimal.

I doubt if the cattle, coyotes and pronghorns would miss being recorded with the thermal imaging cameras for one day.