I received the message in my main account and marked the message "Ignore future messages".
Next I tried to send another message using the same conversation "thread" which still showed up in the Inbox of the test account.
I was allowed to send the new post to the conversation. No error message popped up to tell me that the message would not be read.
There was no notification of a new conversation post in the account I sent to.
The problem as I see it is that when you send from a conversation which the other member "ignored" there is nothing to tell the sender that the message didn't go through. I see that as being problematic. Or perhaps I am missing something?