If you know the person's twitter handle, its simple to search for them. People coming from centralized systems, don't realize that you have to include the domain for fediverse searches to work. I couldn't just find you by searching for p03locke, I'd have to search for @[email protected].
Also, if my instance has never interacted with you, your profile probably won't show posts when I find you (though this is a choice and I don't know why implementations won't fix it.)
Again, instance blocks makes this more complicated because my instance could block yours or yours could block mine and that would prevent this search from working but the user wouldn't know that.
If your instance is already aware of that user, you don't need the domain. Mastodon.social is the oldest mastodon instance and probably the biggest, so it is aware of a large majority of the fediverse.