Have they capped any of the honey? Yes, it'll save time. Is there any drawn comb in the new box? If not, definitely pull a frame of honey and move it to the empty box. That'll help to get them working on drawing out comb. You definitely don't want them to start backfilling the brood chamber, because they think there's no room. Sounds like you've got a good flow. You should get another box or two ready to go.
I used to 'bottom super' from time to time....until small hive beetles arrived. I lost a couple of strong colonies to 'em and I blame bottom supering. Bees will protect their brood from in hive pests but are less protective of their stores. If you isolate those stores from the brood area it'll only give the beetles a better foothold. In areas with shb...I recommend against it.
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