In theory, yes, but thats usually not recommended. When making queens from your eggs, you want to set up something called a cell-builder, which is a queenless hive with TONS of young worker bees that can produce as much royal jelly as possible. The queen larvae is fed something like over 1000 times per day and that requires a lot of bee-power. Once the queen cells have been capped however, then you can put them in any size nuc that you want.
What akadamee says is true, especially if you are trying to raise several queens. I find that a nuc made with one frame of eggs and young larvae, two frames of capped brood, one frame of stores, and two good extra shakes worth of nurse bees will produce a suitable queen. Heck, based on my experiences, even a good one. Weaker nucs though tend to produce smaller queens and that is to be avoided if possible.
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