I'm back up in Deadhorse and just did my first run on the sprained ankle. It did hurt, but felt pretty stable. I did find that I had to wear the ankle brace because even walking without it was too painful. But I really didn't have any problems with running. I could feel a bit of pain, but it felt stable. I ran most of the run at a 10 minute mile, which made me really happy. However, I did keep it to only 3 miles since I am not sure how my ankle might feel when the Advil and the endorphins wear off! I have it packed in snow at the moment, which feels awesome.
Judging by how this run went, I think I will be able to get back into shape quickly. It will probably help more than hurt, forcing it to move. I have to get my speed up for the Paris Marathon which is only about a month away now.