Is a GIST index on a geometry point useful to speed up a spatial query?

I have multiple tables with point geometries and a GiST index eating many gigabits of space. From what I understand about GiST indexes on polygons or polylines, it will store the bounding box and compute a first calculation on the bounding box instead of the full geometry resulting in faster processing. But what about point geometry? Will it do anything more than ordering the points spatially?