Can postgis for postgresql support complex geometric types like spheroids?
PostGIS supports spheroids defined in WKT .
As an example, this section of the ST_length_spheroid page shows how a spheroid is determined, as well as using a sample.
As with other complex types, PostGIS supports almost all types of GEOS geometry.
There are some functions in postgis that are perceived as input, and I'm sure you can define your own (spheroid (or ellipsoid)) http://www.postgis.org/documentation/manual-1.3/ch06.html
Yes, it supports Spheroids, and in general PostGIS has much more complete capabilities than a similar offer for MySQL. I use PostGIS for this: www.trailbehind.com.
PostGIS documentation sucks.