I don't remember for sure if anyone has tried this under linux with wine, but if they have, I don't think it worked as far as I know. And if it didn't work it was probably related to DirectX... I'm not sure how well wine supports DirectX. But it might be worth a try because 1) I don't remember if anyone has even tried, and 2) if they have, it was quite a while ago and both DirectX and wine may have improved.
Hopefully games created with SGDK2 will be slightly more portable, however, I don't have any solid plans to support linux with SGDK2 either. But the fact that the IDE and the produced games are coded in C# should be a step in the right direction. It still uses DirectX, but it should be easier for someone to just write a replacement for the graphics/display layer than it would have been in 1.x. As far as the compiled games are concerned, they could probably even be ported without rewriting any SGDK2 code, just changing the custom code embedded in the project file.