I have the same insurance,I did my surgery on the 16th and haven't gotten a bill so far.My doctors office while starting this journery did say to save between 3000 and 5000 dollars.
You need to find out if your particular plan covers the surgery or not. I have UHC as well, however, my plan excluded the surgery so I am having to hope that my DH's insurance will cover it as I have it as secondary. Good Luck!