It seems to me that the horcrux doesn't need memories. The stored fragment of the soul serves not as a means of resurrection, but to sort of "anchor" the soul to the living world. So the main part of the soul, the part that stays within the living body until death, is left to linger. There is evidence for this: in canon, the first time Voldemort dies, his soul still lives, gathers strength, and then gets a servant to help him, without any contact with the horcruxes.

And I expect that Voldemort actually planned on making Harry a horcrux; what better protection against a prophetic rival than to make him have to suicide to kill you?