Shooting coated case ammo in the AR rifles does require a bit of foresight on the shooter part.

First off, the coating will scrap off the case in tiny amounts and becomes powderized fouling (think of it as trace amounts of graphite).  As this powderized fouling builds up in the chamber, the spent case is more surfaced tensioned bound to the chamber walls, and it this additional tension/fouling binding is strong enough, it will either cause the B/C's inertia to be slowed/lost to the point that the rifle will short stoke, or even worse, the case is stuck in the chamber.  Like gun powder fouling in the rifle, CLP will help to prevent the case coating powderized fouling to build to the point that it will cause cycling problems in the rifle.

Starting with all the upper bearing surfaces coated with a light coat of CLP, the rifle should perform without problems for several hundred of rounds. But depending on the rifle/chamber, you may find that pulling the B/C every 200 rounds to apply a fresh coat of CLP to it, then working the CLP coated BC in the action a few times to all it to migrate threw the action, will solve most of the problems assisted with the coated ammo problems in the AR rifles.

Next step to remember is that CLP or any other copper solvent will not dissolve or break down Polyurethane or lacquer.  To remove this type of fouling, it must be scrubbed out when cleaning the rifle.
Note: Acetone will dissolve these coatings, but will also dissolve the plastic parts use on the rifle as well.

To sum it up, the rifle should be cleaned and lubed with CLP only, and when copper solvents are used to clean the bore, these solvents should be flushed from the rifle to prevent them and the CLP to mix; leading to a gummy mess that will only collect fouling even faster.