You don't need a reservation for them to verify what they were asking for.
Adding the membership to the wallet involves using the Disney MagicMobile feature in the WDW app, accessible from the "Tickets and Passes --> Add to Wallet" part of the app. When you do that, it creates a card in your wallet that lists your affiliations like "DVC-Y" and/or "Annual Passholder" and also has a QR code they can scan to read that info. The only thing that does for MM is confirm you are eligible for the Blue Card benefits (DVC-Y), which is needed to access the event. I suspect if you created a temporary card online from the DVC website (good for 30 days) that also says "DVC-Y" and printed it, that might also work if combined with an ID, but it's not something they can scan so it may slow things down.
But all that is independent of having a reservation in place. The reservation just gives you a higher probability of getting a ticket to the event during the early registration window. Otherwise, without a reservation, you get to try only during the general registration window, which has much fewer tickets. But as a DVC-Y member you can still go to MM regardless of how you scored the reservation.
