“User connects via VPN XYZ” is part of the fingerprint. It doesn’t protect you from identifying you, instead it ads to the number of unique properties of your computer and connection, adding to the size of your fingerprint. Besides, a lot of VPNs and proxies add another header x-forwarded-for with your original IP. Source: I worked on multiple e-commerce platforms that use fingerprinting as part of their fraud protection. Also see https://coveryourtracks.eff.org/learn for a more detailed explanation.

Doesn’t matter, your browser will be fingerprinted with some embedded JavaScript that works in all modern browsers. Detecting VPNs is also trivial.