Discord will publish public-channel messages to search engines from mid-December (discord.com)
Admins can pick which channels participate or switch them all off, in Server Settings under Web Presence, and members get a single toggle in User Settings under Data and Privacy. Public channels are on by default, except member settings default to off in the EU, UK, Canada, Brazil, Australia and South Korea.
The thread worried less about Google than about who can be linked back.