Well to tell you the truth it depends on the radio station. Commercial Band broadcasters would do more contour checking then I would working at a Non-Commercial station. It would depend on listenership as well. If one of my listeners calls me and says they get nothing but static or someone else is broadcasting on my frequency then I would get involved. I don't have the equipment to locate a rouge transmission but I could get it easily enough. Or use my spectrum analyzer I do have and play with it a bit to get a bearing on the transmission. And yes if I find the location of a pirate broadcast I will call the cops. A pirate station in Orlando just got busted a few weeks ago. These pirates last a few weeks maybe a month or so and run like a normal radio station except for the government regulations so their overhead is lower. That and they don't pay royalties. Some don't make money but others actually have advertisers and make some cash along the way.
The hardest part about finding the rouge transmission would be knowing it existed. I cover a large area in 4 different states. I can't drive that distances on any normal basis. The most I do is a yearly contour check and that just on the major highways in 3 directions. (ocean is to the south so no checking that direction)
Again if a listener complains I think even without the best equipment I could find you in less then a week. Maybe even one day. I one of the guys here is a ham and if he puts the word out I bet we could have some bored ham junkies tracking for us as well. In a rural area where your going to affect like 5 people you might never get caught. In downtown Pensacola or Mobile, I'd find out rather fast and cops would be involved.