I've wondered if it would be possible to have the New Posts page automatically refresh when a new post was made.  It would probably be disabled by default, but it could be pretty useful.

Would it be possible?

I am against the idea. It would:

1) Make it extremly hard to use OmnomIRC from there
2) That page is kinda demanding on MySQL. The script was meant to display about 20-30 new posts, yet we use it for 200. If many people leaves a few copies of that page open while they're busy, in the end this could slightly impact on site speed on hours where the server Omni is hosted on gets a lot of traffic.