It can certainly be done. Haven already does this for a specific pubkey: it imports, stores, and serves all notes written by the relay owner or in which the relay owner were tagged by someone in their web of trust. It works by subscribing to a configurable list of other relays, much like a client would. In V2, it will also gain the ability to whitelist and import notes from more than one pubkey.

A relay could also try to fetch all notes from your followers. It can even use the Outbox model to figure out where to download notes from. In fact, this is a feature that has been requested for Haven itself. I’m not sure if any specific relays already implement it, but I think nostr:nprofile1qqsd6ejdteqpvse63ntf7qz6u9yqspp4z7ymt8094urzwm0x2ceaxxgprdmhxue69uhhg6r9vehhyetnwshxummnw3erztnrdakj7qguwaehxw309a3ksunfwd68q6tvdshxummnw3erztnrdakj7qg3waehxw309ahx7um5wghxcctwvshskcpe2h once mentioned she had a way to do this for specific npubs and therefore didn’t need client-side follow lists (was it with Citrine?).

The same caveats described above still apply, though. My Haven database export plus Blossom data is several gigabytes. Even with CDNs and heavy caching in the middle, Nostr + Blossom is often enough to saturate my link. I certainly wouldn’t be able to run this from a mobile relay. So, basically, you need to “connect the edges” of the social graph through relays carefully, consciously of the tradeoffs.