Oddbean new post about login | logout but without outbox people won't find you in that new relay you just disappear
No, because the notes self-propagate.
What outbox does is tell them where to find ALL your notes. As soon as you interact with other people, SOME of your other notes move to their relays. And then large relays they use start attaching themselves to yours, as soon as they know it exists, like nostr.band, Primal cache, Damus, etc.