Will water allow salts to be dissolved in methanol (that are otherwise poorly soluble)?
This is a highly complicated question, and the answer can't be derived by logic alone.

Maybe the liquid phase will remain mixed, and just dissolve some salt (more than would dissolve in methanol, but less than would in pure water). Or maybe it will separate into water-rich and alcohol-rich layers, with nearly all dissolved salt staying in the former. This may be considered an extreme case of salting out.

I know for sure that separation does occur in water/ethanol/$\ce{CaCl2}$ system, even though ethanol by itself is miscible with water in any ratio, as is methanol. Then again, $\ce{CaCl2}$ is much better soluble in water than $\ce{NaCl}$, so the latter might not be strong enough to produce the same effect.

The bottom line is that you can't tell for sure until you try it. Chemistry is an experimental science, after all.