Actually a theory I've proposed about the Mero covers this very issue. You see, if Neo found a way to copy himself, he would copy his being, but he would not copy the unique code that makes him the one, since it's something that's hardwired in his brain, not something that was placed in him. It was his subconcious choice to refuse the programming of the Matrix. If he made a copy of himself, we also do not know if this copy would be anything more but a Smith type program (because it would have to remain a program). I think it would be possible - but I think it's very improbable.