Does bbPress update posts automatically using AJAX?
No.
As I recall it used to a really long time ago, but had the feature taken out or turned off.
If this feature is not currently supported, do you think it can be easily done?
Yes.
It is though a fairly straightforward thing to implement, but personally I’d advise against it. AJAX has been around since IE4 and the MSXML4.0 upgrade, and there’s a reason why it’s not used as often as it’s propents think.
Given how much AJAX posting requires being tied in to a specific HTML markup, and how realistically you’d want to NOT be tied into the horrific Kakumei markup, you’d really just be adding to your own forum(s).
As I recall it used to a really long time ago, but had the feature taken out or turned off.
That was actually when you yourself add a post and it would get added via AJAX.
If this feature is not currently supported, do you think it can be easily done?
Yup, P2 theme for WordPress also checks for blog/comments updates via AJAX so it should be easy for bbPress too.
