Yes, there's a callback mechanism for this, where you can configure callback plugins in ansible.cfg (or the environment) and intercept arbitrary events.
This was an example:
(Though the log_plays setting in ansible.cfg basically does this now, making this above plugin mostly optional)
This one is more entertaining:
So yes, you could definitely route this to hipchat instead of using the notification plugin.
Should you develop a cool script for hipchat, send us a pull request and we can ship it in the callbacks/ dir!