Either diary Tom Riddle -- a manifestation of the diary which was a Horcrux --
would have been a Horcrux himself when free from the diary, or while,
yes, a product of a Horcrux, he would not have been a Horcrux once he
was free of the diary.
But, which would it have been and why?
He would still have been a Horcrux. The diary would, most likely, be emptied and have become a normal diary - I say this because, so far, we have never seen evidence of souls being cloned, only divided. So:
- The soul could not divide (complexity of spells and requiring murder to perform the division)
- The soul could not clone itself (no evidence it is possible at all)
- Therefore, the soul could only move.
Move where? To a brand new body and leave the old diary behind. Thus, the Tom Riddle that is seen would still be the horcrux itself and the diary becomes useless.
To have a body means nothing: this Tom Riddle would have still been a horcrux. Perhaps, he would have become more powerful than the normal Voldemort (if only he had as much experience as the original): this "body" would share the properties of a normal horcrux, meaning it would be nearly indestructible.
For example, if one were to rip a page from the Horcrux diary, would
that page on its own be a Horcrux? Or is a Horcrux always a sum of its
parts? The diary is the only Horcrux, I believe, that can be examined
like this. The remaining Horcruxes were all inanimate objects, aside
This scenario is not possible. A property of the horcruxes is that they are extremely hard to damage - if they are indeed damaged, then they "break" and are "destroyed" and no longer are horcruxes.
You should not be able to rip a page of the diary with your bare hands. If you did it with, say, Gryffindor's sword, you would be able to do it - and the horcrux would be no more since you managed to damage it.
To reinforce this, I'd like to say that it was unlikely that we could have ended up with two horcruxes:
Murder is not the only requirement. It also needs a complex spell. Clearly, Tom already knew the spell, but I doubt he would have tried to do it, because:
- It was risky - he simply did not know the result of splitting himself (an actual horcrux) again.
- It was imprudent - the situation was crazy, he was merely coming back to life - why rush things into making yet another horcrux? He can do it later, preferably once he gets out of Hogwarts.
- Up to this Tom's knowledge, doing so would break his "seven-horcruxes-lucky-charm". I'd hate to have 8 instead of 7 :)