You say “second brood box”. Does that mean that you have 2 brood boxes with a Flow super on top? If so, what is in the first brood box? Empty space? Brood? More queen cells? My first thought is, why did they swarm? It is quite common to have a primary swarm, and then a secondary “cast” which is a smaller swarm. It is a normal way for bees to reproduce. Unfortunately for your hive, the first swarm may take more than 60% of the population with them, and the secondary will take a lot more of the remaining bees. However, there must have been a stimulus, and I am wondering whether they had run out of space or become honey-bound in the brood boxes. If you don’t inspect frequently (at least once a week) in early spring, looking for queen cells, you are accepting a big risk of swarming. If you see queen cells, as you did, you may want to consider making a split, as Marty suggests. There are a couple of good articles about swarm prevention here:
http://www.wbka.com/wp-content/uploads/2015/04/wbka-booklet-english-PDF.pdf
http://www.wbka.com/wp-content/uploads/2015/02/Swarm-Control-Wally-Shaw.pdf
OK, now to your questions. Will they cap the honey? They will if they want to. Sometimes they don’t. If there is no brood in the frame, you could test the honey with a refractometer and extract it if it is less than 18% water. Refractometers for honey are very cheap on eBay and Amazon. Moving stores around takes quite a lot of bee effort, so I wouldn’t expect them to move it much until the colony size has recovered from the two swarms.