"Yes, as long as you do not choose a Negg to open! You can go sign up for Premium and come back to the Negg stash afterwards. As long as the event is running, you'll still be able to choose a Negg and get both a regular Prize and a Premium Prize.
IMPORTANT: If you open a Negg before becoming Premium, there will be no way to get a Premium Prize from that specific Negg—but you can still sign up for Premium and open any Neggs afterwards to get Premium Prizes moving forward. "