If you bought Dark Game Studio you'll only have access to Dark GDK (full version) and not Dark GDK.NET (iirc, .NET was a wrapper written by a third party). So Dark GDK 1.0 is only compatible with C++.
But, Mistrel is working hard on Dark GDK 2.0. Mistrel is a 3rd part developer, so it might be possible you'll have to pay. All Dark GDK commerical users will get a free upgrade and it sounds like that applies to DGS buyers too, but I've not seen Mistrel confirm that himself.
The advantage of 2.0? It's not just for C++, the idea is for it to be useable in a range of languages. At the moment it's got a release candidate and RC5 will have .NET support. There's more information on the Dark GDK part of the forums.
I hope this helps you.