I recently made a simulated swarm that needed two deeps, whereas I usually put them in one deep until all frames are drawn and filled.
This was a big four deep overwintered hive that was well populated with both young bees and foragers. It had a 2012 good queen I also needed to be able to get to for grafting this year. The hive got so big fast last year I never took the time to dig her out to get some daughters.
I moved the entire hive a few feet away and let all the foragers return to the original location where the established queen and two frames of open brood, along with new frames and a feeder with fortified 1:1 waited. The return was so populated I thought it was far too many bees for one deep, but I wanted to get them to at least start drawing the new frames in the bottom box before adding a second one.
After about a day and a half, I checked to see if they were taking up feed and drawing frames. They were, so I gave them another deep. I moved the feeder to the top and gave them a second one as you can see here. After a week almost all the frames are at least partially drawn and the volume of space seems good for now.
I've done this many times. Along wth the frame of brood, a big fat queen that is unable to fly keeps me from worying anymore they will abscond. Your situation is different with a queen that can fly. A frame of brood is always a good idea for inducing a swarm to stay in their new home.
You can always confine your queen for a day or two if abconding is a threat. Theres a lot of options for making it work.