Yeah they have worked with many companies they will explain how windshield replacement has been done and how to go with the insurance companies.Call your insurance even if you do the repair out of pocket to get it done soon. I suspect safelite will tell you that, though. They work with most companies.
I had to repair a big piece recently and learned that all glass is considered no-fault, even if you do something stupid. Covered less you deductable and unlikely to affect your premium.