I think that's absolutely the most likely. And it's not hundreds, it's probably more like tens of thousands (or more). For example, when I got mine issued in Germany, I just went to a pharmacy, gave them my ID and (paper) vaccination record, and the pharmacist came back in a couple of minutes with my QR code.

The interesting thing to watch, over the coming days, is this: will the public policy response do the technically correct thing, and make sure that you need all your original documentation (signed records from the doctor's office, etc.) to get your new covpass issued? Or will they do something incorrect (but easy), like let people come in with their now-invalid pass plus a government ID to get a new one issued?