It's a breeze to get regular homework done even with FIRST, but that requires killing most free time. Big projects however, are near impossible. The last one was a presentation, and my teacher let me go last (because of FIRST), and I was barely done even a week+1/2 extra time.
I've got a research paper coming up, but luckly most of the work can be done after the build season. If you are overloaded during the build season, don't be afraid to tell your teachers. They'll most likely be reasonable.