I don't have one myself to specifically test. Assuming you're asking this question because you don't have one and are considering purchasing one, the answer is I don't know how they implemented their extra buttons. If they support Direct Input (not likely; very few mice do), then Inner Space will support it through Direct Input. Otherwise no, not yet

If you do have one, then the sticky
[Input Devices] General information and supported hardware has a link near the bottom that can provide me with the data necessary to add your device to Inner Space. However, again, very few mice will support this method either.
Most mice have their custom buttons implemented as a separate full Keyboard device and use their drivers to program it. They simply do not give us an "extra button" at this level.

(Not the end of the world, I have the solution for this already implemented in the next generation of Inner Space)