It could, if we say that consciousness (I'm still not sure how that word is thought of here) is thought to be a physical object.

If you don't understand consciousness then this isn't allowed.

However, (and I am saying this tentatively), I've heard of instances where particles can be made to have no distinction, where action on one particle has effect on a particle at a distance, so there is a prior example of two physical objects being the same entity despite spatial and numerical difference.

Do you think that if we had turned out to live in a purely Newtonian universe with no quantum nonsense then no-one would have proposed Open Individualism? If not then the resolution can't lie in quantum physics.