It really depends on your implementation... our authentication systems has a unique user GUID (not the mac address)... When the user logs into the site and every page/action they visit or interaction with while they are logged in, I capture that GUID in an eVar. If the user doesn't log out, that GUID is captured when they return to the site. When they log out, the GUID is cleared from the systems and subsequently from tracking. (I know some implementations set their eVar to never expire... but with shared devices, we treat "sign out" like a clean slate. Therefore I rely on passing the GUID on each call.)
I don't know enough about your implementation to know if what you are capturing is tied to the user's device, or tied to the account... Or are you talking about the user's ECID? which is Adobe's users identification GUID? If that's the case, then yes, that is just your Adobe UV identifier.... You would need to see how your authentication system works, where the data is stored (cookie? session storage? etc) and how to extract it... then you need to know if this is an actual user id, or just an authentication token.
An Authentication Token would be a different value on each log in, and basically acts as an interface between your site and the authentication portal to say "this is a valid login session"... but overall, that data wouldn't be helpful to you.
You may need to reach out to your developers to explain what you are trying to do, and work together to find a solution.