Do you watch Westworld? They discussed similar themes - what is the difference between an android that looks exactly like a human, moves/talks/thinks like a human, and feels pain like a human vs an actual human.
Bladerunner has a similar concept.
Both shows thought that by giving robots "memories", it will help with their sense of identity.
Yes the same principle is applicable there if you imagine that's how they solved the bot memory problem. And indeed, memories ARE identity, in humans too. It's interesting stuff to think about.