Is it possible to add a UID to M45PE10-VMN6?
I doubt it. The datasheet says that:


  The CFD bytes are read-only and can be programmed with customer data upon demand. If customers do not make requests, the devices are shipped with all the CFD bytes programmed to 0.


It's not clear from the datasheet whether the CFD bytes are explicitly programmed to zero or if they're simply left unprogrammed, but either way there isn't any documented method of writing to them.