It's possible, but would require coding and (as far as I can remember) has not been attempted yet, so there's no instructions on how to do it. There have, however, been a couple projects that came close. I think one project showed how you could compile your game to run in a web page, but it wasn't communicating anything over the network, so it wasn't really online -- just browser-hosted. Another project was using a web site to generate snowflake images which were then shown falling on the screen, but that's not very interactive -- just one-way data retrieval over the web. You can talk to durnurd about those projects if you're interested (I don't think they've been upgraded to work with SGDK 2.1).
Basically, I think you would have to implement the online part in the "Source Code" tree of your project as you would if you were developing it directly in C# (.NET). Then you should be able to link that code to your project using the online help that describes the API/framework for SGDK2-generated projects. If you get anything interesting worked out, it'd be cool if you could share your custom code objects as a template that others could import into their projects. What exactly did you have in mind -- 2 player scrolling game over the network where each player could see the other player and their actions if they were scrolled to the same location?