Re: Virgin Queen
If you have a spare frame of eggs, I'd use them. If they need, or feel they need a queen they will use the eggs. You could have had a virgin that left to mate and didn't get back, so in my mind adding the eggs hedges your bet for possible QC's and slow the possibility of laying worker until the hive gets right. Should also give you a few new nurse bee's to help bridge the laying gap.
I'd sure try to locate a queen when you add the frame of eggs, "just to know", but you should see QC's in a few days if they feel the need.
“Never be afraid to try something new. Remember, amateurs built the Ark, professionals built the Titanic”