In theory, yes, you should be able to develop a 3D application using C# and OpenGL on both Windows and Linux.
In practice, this is likely to be somewhat painful: you will need to restrict yourself to the subset of functionality that works for both Visual Studio and Mono, and it is likely that you won't be able to use many tools and libraries which have been targeted at only one environment.
You will need to take a very rigorous approach of converting your project files from one environment to the other, testing early and often so as to catch problems quickly, and rewriting immediately anything that proves not to be portable. This can be very frustrating at times.
In the end, ask yourself why you would want to target Linux. If learning C# and 3D development is your main goal, maybe you should concentrate on Windows instead of getting lost in the intricate details of different platforms. If your goal is to write a platform independent 3D application, many other interesting languages, such as Java or Python, might be better options in term of portability, and they are close enough to C# that you can leverage most of your experience in that domain.