In reply to George Ormerod:
I've ran with a few broken arms. Not so much in a sling for long but in a cast. On longer road runs it was an issue, just the unequal weighting. I tried a 100k and ran ok for 20 miles, but for 10 miles struggled with a hip issue which I think was due to the imbalance on that side.
I found rougher trails were better because you run less uniformly and so the weird imbalance was less of an issue.