Yes. That is exactly what you should do, but only add the second brood box when your first is bursting with bees. I don’t want to type it all again today, but look half way down this answer that I wrote earlier today:
Yes, but only when the first box is 80% full, bursting with bees etc…
You will find it hard to get another nuc without a queen. People will look at you funny. Just use an extra deep box of empty (or wax foundation) frames.