>Question: Will the bees feed the queen through the cage?
Since they are queenright and since this is a super and unlikey to have nurse bees, it's doubtful. More likely they will kill her. But it is possible they might take care of her, just doubtful.
> Will this plan work?
Your plan does not seem to include any brood or anything that would anchor the bees to the new hive (brood will) nor anything that will allow for the drift back to the original hive (like shaking in more bees).
> Any suggestions?
Two frames of brood, two more frames of bees shaken in. Leave them queenless over night then put the queen in. Meanwhile catch four fuzzy bees off of the capped brood combs (young bees are fuzzy) and put them in the cage with the queen until you can set up the new hive and let it set overnight.