If I'm currently on a permanent profile, due to severe osteoarthritis, and require surgery. What's the outcome of refusing surgery?

Why would you refuse surgery? If your condition is that bad, then having the surgery is likely a good thing. If you refuse it, and then get out, I guarantee you, having the same surgery done in the civilian world is going to cost you thousands (if not tens of thousands) of dollars to get.

As for any repercussions... Not quite sure, but if the Army is keeping you in service, and surgery is a condition of that service, refusal might be seen as refusing a lawful order. Now I am not sure if you can be ordered to have surgery, but why refuse something that might help you? If you are really against surgery, check with your local JAG office and/or your military hospital's patient information center.

I feel for you though, as I have the same condition, just not bad enough for surgery. I've been offered cortizone injections, which I refused-- having big needles shoved into my knees each week is not my idea of a good time.

You should not of been allowed to join sounds like somebody did a two step around the rules.
Since you are in take the surgery and this will be a real eye opener follow all the direction after you have a surgery.
I hope someone will follow up on how you made in the Army!

Then you will probably get boarded out.