I don't know that they would make a queen cell from a laying worker egg. In a laying worker hive, they "think" that they are queenright.
Package bees seem to hive a higher rate of supersedure than any of us would like to see. I assume that a package will have queen problems and feed medicated syrup right away in case of Nosema and then I keep an eye on the colony for the rest of the year looking for signs of trouble. I've had one go queenless this year and it was odd. The package arrived with an open queen cage. I shook them in and went back after a week and found brood. One cycle and she was done. No eggs, no brood, no nothing. I re-queened that colony.
"My wife always wanted girls. Just not thousands and thousands of them......"