Did Voldemort inadvertently make himself Harry's horcrux?

Voldemort used Harry's blood to resurrect himself and make him part of Lily's sacrifice so that he could touch/kill Harry.

In the way that Voldemort could not die as long as Harry(and the horcrux) was alive, Harry could not die as long as Voldemort(and the Lily-horcrux) was alive. So, when Voldemort "killed" Harry he also killed the horcrux, which made Voldemort mortal and therefore allowed Harry to kill him.

If Harry had tried to kill Voldemort before he had "died", Voldemort would have come back in the same way as Harry, albeit now Harry would be the vulnerable one, since killing Voldemort would destroy "horcrux", while Voldemort still had his horcrux inside of Harry.

So, basically, Voldemort's fate was decided the second he killed Harry the first time. Sorry if this doesn't make much sense :P