Cloak board or not, I think that it depends on the time of year whether you leave it or not. I normally feed my cell builder hive, so I wouldn't leave a honey super on. But when I am raising queen cells during our flow, I don't worry about feeding and just leave the supers on.
If I have a super on but the flow is ramping up or fading, I would remove the supers and feed.
I wouldn't leave it on for the simple reason that you'll be in and out of the cell builder a lot. Our cell builders have plenty of honey in the bottom deeps and in the top cell builder box. We give them a full frame of pollen/nectar each side of the cell frame and honey outside of those, along with capped/emerging brood. And they get a 1 gallon feed bucket on top. Move the super to another hive temporarily while you're raising queens.
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