No. The ego is best visualized as a computer program that takes in situations and generates a programmed response. The more automated the response, the less you take the time to examine your actions or where they came from, the more we call it ‘ego’.
Freudian psychology distinguishes between three different ‘modes’ of cognition. The id, ego, and superego. The aim of psychoanalysis was thus to work to bring integration to the modes so the person could have greater agency in their life.
The belief that the id and superego aren’t really part of the person is precisely a function of ego, the part of the mind that conserves agency in the face of attack, even from within. The ego will always claim that it’s in charge.
But ‘I’ can only ever refer to the whole person. If your id drives you to murder someone, you still go to jail.