Does adding grey to de-saturate a color, change its value?

The value will change depending on the value of what you add to de-saturate it. A light grey will lighten its value, a dark grey will darken its value.

For example, if you take cadmium red medium that comes straight out of the tube, it will be highly saturated. If you want to make this a less saturated red, you can add white, black, grey or any color that is less saturated than that red. It might become darker if you add black, it might become lighter if you add white (pink). However, in all instances that cadmium red medium will no longer be as saturated, and it will no longer be called cadmium red medium.