you still use the cunningham because that is the only thing keeping the mast in snug and you dont want a broken mast step and it helps keep the wraps neat and you should be able to have all battens in on 1 wrap.
If you don't crank on the cunningham first, the sail will get wrapped up with a deep draft and will be almost as bad as an un-reefed sail. You can wrap once with the batten in, but the batten has to come out for two or more wraps.