For search, we have different search methods. For those that use a search relay or API, it wouldn't matter I believe because you're not searching just your relays. For Damus that is now using a local DB, that would limit search to just what you've seen, so search wouldn't change here either I wouldn't think? These are both speculation and I could be wrong.
Discussion
It will be interesting to see how search on nostr progresses and if it can be decentralized. I mean, web search also sucked early on 😂 but web search is centralized to just a couple providers. Can nostr avoid that?