This isnt how nostr works. Nostr is just how to communicate your messages. Damus and amethyst are the interfaces that plug INTO nostr to allow the free distribution of your notes out into the relay world. Posting on one wont be wonky or not show up on the other. Your private key (Nsec) is what holds your notes (posts) you own your data and share it with which relays you choose. So the relays of damus and amethyst you are connected to would be the only deciding factor on if you posts reach others.