Your problem will be with how fast DL recognizes and updates your status. You may want to print out your account history and status from DL.com before you leave and hold on to your boarding passes. At least this will give you some back-up for the lounge dragons.

I never have to show my PM card at an AF lounge because the boarding pass has Elite Plus printed on it (even with AF) Your problem will be the time it takes for updating the records from AF to DL (for the flight) and then DL to AF (for the status change).