This technique is not possible on Radiopaper. Once a conversation is published — which happens as soon it has messages from both parties — neither party can block the other party or unpublish the conversation (though you can edit your own posts, including deleting them).

Either party can keep adding messages to the conversation in any order, but only a back-and-forth is considered an update to the conversation as a whole, for the purposes of sending it to the top of the feed. That way, if a conversation turns sour, one person only needs to stop replying, and the conversation will gradually sink down the list into oblivion, even if new messages continue to be added by the ignored party.