I was interested in if posting an AJAX quick-edit would show any posts below yours.
Test steps:
1. Opened two tabs. Created a new topic in one and went to the board listing in the other.
2. After posting "Message 1", I opened that topic and posted "Message 2".
3. Without refreshing the first tab, I submitted an AJAX quick-edit. Message 2 did not appear until after a refresh, although Message 3 did appear.