With a weird set up like this we need to be discussing the set up. If used incorrectly our cops can cause more damage to the town then they can help the town. So let's be smart about what we do here.
No we don't. Cops won't do any damage if you take things into account logically and don't RUSH it.
not everyone needs to cop the same person. Thats retarded logic. Say for instance, 7 cops target Mikey. 3 get him as town, 4 get him as mafia. Do you lynch him? It gives no viable info as of that point and by day 2 we can cop ourselves thus rendering the point moot anyway. The better option is to scatter the cops around, then night 2 cop yourself. That way you get 7 results, and know for sure the alignment of 7 people.
* this is of course based on the premise that we get the sanity of the cop when he dies. Thus 7 people can claim their results from night 1 straight away.