Yes, but unless it's literally Lasik, which has a robust private market, your provider will probably literally make a price up on the spot. That happened to me several years ago, when we needed urgently to get a CT scan for our daughter; it was late in the afternoon, the provider couldn't get the insurer on the horn, they proposed to do it the next day, I was jumpy and said "fuck it I'll pay out of pocket", they looked confused and then just made up a price: $1000.