As far as I know about waves, this is incorrect. Changing the sign of vt simply changes the direction the wave is moving in and hence does not capture the idea of a positron. A positron was postulated by Dirac as another solution of E2 = m2c4, IIRC.
I am less sure about this, but wikipedia seems to agree with me, so, what do you think is wrong in considering a positron to be an electron moving backwards in time? AFAIK, this is a fairly simple way to think when using Feynman diagrams.