Brian, I think you missed this part of his post...
>>>>Instead of pulling frames from the deep brood chamber and putting the shallower frames in<<<<
He has a deep brood chamber and a shallow or medium super. They don't mix well.
Yes, it is fine to add the super. You should have enough warmer days for them to rearrange the furniture to their liking.
I did noted the different sizes that's why my suggestions didn't specify frame size, the jog could be done with whichever box he wanted or add another deep if the frozed frames were deeps or add another medium if that's the case. Whichever way it is still doable.