Someone became blind from cataract, would their eye color change?

Might turn white. An advanced untreated cataract will eventually turn white in the pupillary space. If still untreated, some will dissolve and lose the white color but more often will rupture and set up a terrific inflammation inside the eye. In this era, cataract removal is so predictable and safe that advanced cataracts should be rare.
Rare but yes. Cataract surgery is the most common surgery performed in world & US. Complication risk very low; best time in history to have CS:
Never. Eye color (i.e. The brown/blue/green part, the iris) does not change because the cataract is behind the iris.
Cataract. A cataract will not change the color of the iris but if the cataract is advanced you may be able to detect its color (brown or white) by looking at the pupil.