Congratulations, it is such an exciting time.
My surgeon's office has a dedicated person who works with the insurance companies. she was the first to call to let me know I was approved. The hospital bariatric coordinator also called, and then I got a letter from the insurance company. So, don't worry, you'll definitely hear about it!
Once everything was final, I had a last appt with the surgeon to make a date and go over everything one last time, and then I had to go to my primary for a final clearance.
I work for a big company too. I wanted to avoid questions and concerns from co-workers, so I took vacation days. I have a great team of people and they would have been worried if I was out sick for a week and would have asked a lot of questions out of concern. I can't lie to save my life and would have wound up telling everyone about the surgery and I wanted to keep it private.
If you are taking sick days, you may be asked to supply proof of disability. FMLA doesn't require a diagnosis, so there is no need to mention any details unless you want to.