No, that's not the whole point and I struggle to understand why anyone would want that. If you want to run a server that does Nostr on your behalf it's better to get it to serve you only the notes that you want using a custom API only between you and it.

Nostr clients are made to talk to multiple relays -- and to not trust them, and to bypass their censorship attempts and go find notes elsewhere etc.

But the approach above is still valid. If you use something like Ditto, for example, it will download notes from a bunch of places for you, then serve them to you in a neat and efficient interface.