Fighting for coverage but still having surgery question

I was declined by my insurance company because according to them it "isn't medically necessary in my situation" despite the fact that my BMI is over the cutoff.  Apparently, part of the decision is based on something the nutritionist said so I will be calling the office on Monday to find out what was said and if it was something fixible.  I have a surgery date and its perfect with my work schedule and I really don't want to cancel it so I'm contemplating cash pay.  If I have the surgery and pay for it before the insurance situation is resolved can I still fight for them to cover a portion or am I screwed?  I have BC/BS Anthem in California. 

Most insurance companies have BMI cut-offs at different tiers.  So if your BMI is above X but lower than Y, you need to have other conditions such as diabetes, sleep apnea, hypertension, and others.  You may be able to get the insurance company to cover you at a lower BMI, but you'll need help from your surgeon to push the insurance company to demonstrate the medically necessity.  The devil is in the detail on this one.

I would not self-pay for a surgery like this for which approval had denied and expect to get money back from the insurance company after the fact.  Not saying it can't be done, but will be a rather painful and possible expensive endeavor.