If we put an metal electrode in water with no metal ions present potential should tend to minus infinity?
Yes. The potential is in principle infinite if the water is pure. But in reality, when a metallic plate is dipped into pure water, you cannot prevent one or two atoms from being oxidized by air and pass into solution. On the other hand, the same thing can be said about $\ce{O2}$ producing one or two $\ce{OH-}$ ions. As a consequence the potential goes quickly from infinite to a finite value.