I downloaded the C# demo and I see that it is using OpenGL.

My application requires use of DirectX11. Is it possible to use the C# API with DirectX11?

Sure, I don't see why not. Create a SharpDX.Direct3D11.Device instance and pass the unmanaged ID3D11Device* to Noesis.GUI.InitDirectX11 function via the device's NativePointer property.

Effectively, the C# API is compatible with OpenGL, DirectX9 and DirectX11. Although the sample included inside that SDK is only OpenGL.