Yes. You might have to extract a sheet body from the face temporarily. And are you looking for the geographic center of the face, which ignores the holes in it, or do you want the center of mass - the point on which you could balance it, so to speak?
We can do that with UF_MODL_ask_mass_props_3d, which is also wrapped for use in .Net.
Do you have a preferred language? I'll try to find an example.
Here is a basic example in C#. A couple of things to note - you might want to use different units, and you can do that by changing which massUnit assignment is uncommented.
Also, this function is a bit peculiar in that it returns the output info relative to the WCS, rather than the Absoluted CSYS, like almost all other NXOpen calls. I will probably add a few lines to do that, and then I'll post it to our online samples in a day or two.