I think that's an oversimplification of what GP was getting at.
Tuvix was an accident, knew and accepted that fact, and initially was voluntarily assisting in finding a way to undo it. He seems more than capable of grasping, even at that early point in his existence, that undoing the accident means the end of him.
GP made the argument that his demeanor started changing as he got a name, a job, responsibilities etc. All the superficial hallmarks of a "person" in the very limited environment of the ship.
Nobody is saying he wasn't a person from the start, but getting assigned all the trappings of what he saw to be individual persons undoubtedly started him thinking of himself as a person as well instead of just an accident to be corrected.