Yes, it does, except you're not tied to a single Mastodon server nor they own your identity.
Discussion
i agree we need to make relays less faceless. for example if you're a Nazi like me you only really need relay.mostr.pub because that's the one that goes to Fedi where all my frens are - but it took me MONTHS on here to figure this out.
instead when you're signing up it should help you find the right relays. it should ask you - do you love Hitler ? if yes then this is the relay for you here. etc.