Not really, each user is centralized at each instance. So firstname.lastname@example.org is different from email@example.com for example. The difference being that despite the separation, I can communicate between them and anyone else on the Fedverse via my own login.
The best way to think about how mastodon works is sort of like e-mail, it’s a ton more immediate but which site that I am signed up to doesn’t matter so long as I have the e-mail address, mastodon’s user addresses (firstname.lastname@example.org) work in the same manner. Me being on mastodon.social doesn’t keep me from commenting on things with users of cyber.space, niu.moe, pawoo.net, etc. because they are part of the same network and every user on those sites has an user address that I can contact them with in the public forum.