If I interpret the homepage correctly clients/servers without extra COI enhancements will just receive the messages as emails. Not ideal, but in any client with threading (gmail, apple), it would work decently i guess.
So an existing server need not do anything to support COI clients. But a malicious server could easily decide to reject them, or to filter out COI-specific stuff from messages. I don't think it's likely, but it sometimes big corporations and governments get paranoid about weird things ("network load!!1!") and take technical measures to block them.