I did my scaphoid in a mountain bike accident, took a week to diganose (when I lost the strength to push forward to change gear, it finally registered on me that all might not be well...)
I had no surgery, but all healed fine. I was told to staf off the bike for 8 weeks, but energy was still fine and could use static trainer. I think running should be fine, but same issue - if you fell and re-impacted the break it could be made worse. So training might be tricky, but I think healing should be fine. Mine is now 15 years later, and I've never noticed it since.