This varies greatly by state, as each states' laws govern what is essential vs cosmetic medical procedures. For example, my work insurance is based in Tennessee, and all bariatric procedures are 100% cosmetic, so no coverage at all! To further complicate things, individual companies within these states can have varying coverage depending on how much business they get from your employer. Even if a company like Blue Cross or Aetna cover it for employees of one company, they won't for others.
You will really need to look into the offerings you have available, and call them directly. You may have to get assertive with them to get a straight answer. I had one make me go through programs and jump through hoops to prepare for it, only to tell me they wouldn't cover anything when I went to schedule surgery. One even told me they would not cover any future medical procedures if I have it done anyway!
I'm with another company and insurance plan now which didn't cover it either, but they didn't blacklist me for having a self-pay procedure.
Good luck, hopefully you're more successful than I was with the insurance company.