Yeah, unfortunately, it does. It's free (at least for now) for Blackberry and (I think) Nokia phones, but that'll eventually change I imagine. It comes down to how badly you want that little "extra" experience, I guess. I think it was only like $3, though, so it's not terrible. A free option would always be best, obviously. I'd probably pay for it, just because I visit a lot of forums and I know a lot do use it.
But the full page version! That's a great idea, definitely better than having two pages open, like you said. Auto-reloading would obviously be ideal, but that has nothing to do with you or the chat plug in thing. It's definitely a good option, though, for the mobile chat. Just bookmark the full-page thing and you've essentially got it on hand all the time.
Also, I think (from the very limited research I've done on it) that most smartphones nowadays should be supporting AJAX, it just comes down to the browser. Like I said, on my Blackberry, the Blackberry browser doesn't even load the chat, but the BOLT browser has no problem with it. So, for those of you that want the chat on the move but it doesn't work, make sure you're trying other browser options.