It may slightly shift undertones, but it’s not going to go from a blue-gray to a brownish grey.
(the reason for the shift is that color and pigments aren’t linear at all concentrations)
Adding white is different from cutting the colorant load. It can take A LOT of white paint to significantly affect a color. It depends.
Whenever you cut an existing formula, you’re creating a completely different color. It’s not the same as creating a color string. Color strings are a continuous range. Often starting with a saturated color moving in regimented steps all the way to a neutral gray. There’s usually a goal to change only one color aspect along the string. E.g. only change saturation but not hue or brightness. Only change brightness but not saturation or hue.
Tangible examples you can check out: Benjamine Moore’s Color Preview deck the color strips are strings. Benjamin Moore’s Classic Colors deck the color strips are NOT strings.
Since brightness and saturation are inextricably tied, it is very difficult to create color strings. And it’s highly unlikely to happen at a paint store counter.
When paint color formulas are cut at a paint counter, original colors are not being adjusted. Rather new variations of the color are being created. Due to substance uncertainty of bases and colorants, anything can happen. Won’t know until you mix the color, let it dry and then look at it.
People believe that cutting a color by 50% is going to get them a color that’s exactly half as bright and half as saturated so that’s exactly how they see the resulting color. Because it sounds logical. However, the reality of what happens with paint bases and colorants doesn’t always align with logic.
If you were to measure that same result, either by qualified observer or device, the outcome would very likely NOT be a color that’s half as bright and half as saturated.