Not if they already have a queen, but if there is no queen they
will draw out queen cells from eggs in the frame. If there are no
eggs, they will select very young larvae that are no more than
three days from hatching. If all larvae are older than this they
bees can't make queens.
In an emergency, if a hive is suspected to be queenless, a
beekeeper will often transfer a brood frame with eggs from another
hive to get the colony going again.