No! And here's the trick. SEO != regular user.
When a regular user goes to the forum page A they'll get the HTML for
page A but when they go to page B, the HTML will still be for page A.
Since it's AJAX, there's no reload, but as you've noticed the HTML is
out of date.
The trick is that this doesn't matter! The only thing that matters is
that the google-bot is able to reach every page. It will follow all of
the links on the page, and reload them as separate requests (no
javascript, so no ajax) hence getting the right HTML for each page. To
make sure this happens right, you need to make sure that the links
render right and that you have real <a href> tags, so the googlebot is
able to spider everything.
good question,
-Jeff