So, theoretically, during the install, you could present a SN of another unit (say Fritzbox) and ask Openreach to register the number of that new unit, no?
In theory yes, in practice no, as they only support using their own ONT so you have to clone the details of their ONT.
Remember, the demarcation point of FTTP is the ethernet port on the ONT. Replacing the ONT is like replacing your master socket, it is officially absolutely not allowed, but there is nothing to actually stop you doing it. But if you make a mistake and it caused problems for other customers, you're potentially in a lot of trouble.