There is no question about it, if they are queenless and you add a frame of brood and eggs, they can make a queen like Ted said. It will be about 30 days til the new queen starts to lay.
If the sound you hear is a signal they are about to swarm, a frame of brood won't stop the swarming impulse. You will need to do something to make them think they have already swarmed.
But first, you will have to look inside the hive. Look for evidence of queen activity...Are there any eggs? Any larva? Any capped brood? Any queen cells? Once you answer those questions, you will know if they need that frame of eggs and brood or not.
If you find queen cells you will need to split them into two hives. Leave two queen cells in one and the queen in the other. Iddee would try to save most all the queen cells, but that makes it more complicated than it needs to be for you at this time. Just leave two cells alive, kill or give away the others. HTH
