Usually I'd agree, but it would make for a nice change and add a sort of "meta" level. The game would react to what you're doing, and with your "clone" working against you in the background unseen. You could collect clues on wether you are a synth or not, and have to decide in the end what the difference is, really.
This whole "the game reacts to how you behave and confronts you with how much of a monster you are" has already been done in Deus Ex, of course. Would be fun to have it in a Bethesda game, where the normal mode of gameplay is "genocide", and where in the end you meet "yourself" who is very sad that you, the player, became a mass murderer.