In a sketch, is it possible to mate the center of a circle around the centroid of a selected body?
Sure. Use one of the macros that makes a 3D sketch point at the CG of a part, and then make a plane and a circle related to that. macros at this site: http://www.frontiernet.net/~mlombard/ matt.
Realizing it won't be parametric. If you modify the sketch you will need to generate a new point, etc.
If the macro is used in a macro feature, the 3D sketch point would be parametric and update with changes to the part.