Wow, search is coming to Mastodon and privacy options are simplified!
IF your profile is discoverable (findable by name, not account id, and visible in Trending toots), AND your toot is public, the toot will be indexed by servers where text search is enabled (enabling text search is optional feature and carries a sizeable data processing a storage cost for the server). Whether your server enables search or not doesn't matter - other people's servers do the indexing.
Edit: the plan to reuse an old discoverability setting has been changed, search indexing will be a new setting. The critique I had here is no longer relevant.