Dude, the cops might do anything, but its very very unlikely a Cop bait girl will have a history, either on TER or just adds on Backpage or where-ever. Think about it, they open a phony profile and bust 10 guys who show up at the hotel room day one....repeat day two....what's the liklihood that this one profile wouldn't get exposed? And why would they bother, just set up a new one each day/sting, it only costs them the cost of a new disposable phone. When I got busted, the add was down by the time I was released and checked for it.
Also, no guarantees, but: Cops less likely to send bait girls to an Outcall then to have them do Incall. Incall allows them to set everything up the way they like it, make sure the lady cop is safe, efficient use of manpower to nab multiple Johns in one net showing to one room. Why send a girl, her takedown squad back up, etc, all drawing OT on the clock and taking up multiple vehicles, out to bust one lone John on a misdemeanor in his hotel room? It would be like picking one car on the road to follow home to see if he speeds...not an efficient way to rack up arrests for a low level crime. they want deterrance and hi volume.
Also, no guarantees, but: Lady cops are very unlikely to have long chatty ads, to have multiple pics showing faces and naughty bits, to have changing pics over time. Also, unlikely to display paranoia about you being a cop...last thing they want is to get you focused on the idea COP. Also, unlikely to have even a history of ads in one day, am thru pm, or offer 24-7 service. Cops work shifts, and get OT, and they don't want to wait on some guy to call for a 7am or 4 am apt...you're not the Medalin drug cartel, you're just one of mult Johns they want to round up in a quick Sting.
COPS signs: asks you what you want on the phone or in person (by the time its in person, too late, no way to avoid being busted). Price too good to be true. Pics that show neither face not the good parts. NO HISTORY ANYWHERE.