I've read the documentation (sales brochure) on 3DGS, and yes I understand that it uses C-script, a C++ like language for its main programming interface. It also states that you can also use C++ Builder or Delphi through external .dlls.

My question is Can a C# language be used as well with the system?

Theoretically any language can be used because the Gamestudio engine is just a DLL. However the included headers are for C++, and some users adapted them to Delphi. but I don't think someone adapted them to C# yet. So I think unless you want to do that yourself the answer is no!