Our VB.NET project is using a Java library from Vivid Solutoins (com.vividsolutions.jts.geom.Geometry) to do Geometry calculations. The help is here: http://tsusiatsoftware
First of all, I don't know this API, I've just browsed the link you've given.
Judging by the Javadocs for Coordinate, it says:
[Coordinate is a] lightweight class used to store coordinates on the 2-dimensional Cartesian plane. It is distinct from Point, which is a subclass of Geometry. Unlike objects of type Point (which contain additional information such as an envelope, a precision model, and spatial reference system information)
So it would seem that Geometry has no units as such, but Point, its subclass, does, and you can specify them.
I wouldn't be surprised if the Geometry class doesn't have any units as such, and just represents the concept of a point in space in any particular coordinate system.