Yes. All NURBS surfaces are essentially like a rectangular rubber sheet with 4 sides. The sheet can be stretched and twisted in any way but the basic ‘rectangular’ structure remains - the “U” and “V” directions that Martin mentions above. There is one possibility to collapse one or two of the edges to zero length to create ‘poles’ - this is how one can get a sphere or a cone, or even the flat circle above (which is actually just a ‘flat’ cone). But aside from the collapsed outer edges, the rectangular UV structure always remains.
There are however an infinite number of surface configurations that cannot be represented with just the ‘natural’ untrimmed edges. A simple example would be a planar surface that has more than 4 edges. This type of surface cannot be defined as a single untrimmed surface defined by its natural edges. It can only be described by a trimmed surface - one where the natural edges have been cut away by the outer border, or, it must be broken up into several joined untrimmed surfaces that have four natural edges or less.
It is for this reason that it is very important to understand the difference between untrimmed and trimmed surfaces and their respective properties and roles in Rhino.