It isn't clear from canon if a single horcrux turns one into an easily recognizable monster. We know that Voldemort looked like a monster after he had 1) made multiple horcruxes 2) was killed and then came back using dark magic.

In fact, we know that when he was Tom Riddle he had already made a horcrux when at Hogwarts and he still looked like a normal human until at least the end of his time at Hogwarts.