Yes, it works for any approximately spherical surface regardless of size. The way it works can be thought of this way:

In a normal cylindrical projection (Which Mercator is), the length of one matching pair of parallels (or the equator by itself) sets the width of the map, and all the other parallels are stretched or squashed to the same length. The poles, both of which are just single points, also get "stretched" into lines this length. If you leave the north-south distance alone, you get a projection called "Equidistant Cylindrical" or "Equirectangular". If you want to preserve angles though, you need to compensate for the east-west stretching which you can do by also stretching north-south by the same amount. This has been compared to inflating a balloon inside a cardboard tube coated with glue. This is the Mercator projection. It turns out which pair of parallels you choose to start from aren't important in Mercator as it does nothing but scale the map up and down without altering the shape. (This is not the case for other cylindrical projections.) Since no finite amount of scaling will stretch a point to a line, the poles get pushed to infinity which is why Mercator maps never include the poles.