BeeJive's push notification currently consists of sending an email to the address of your choice. If you don't have push email, the notification will not be immediate. Separate from this, yes, you will be connected 24/7 (configurable) no matter what IM account you use.
Thanks for the update! So it emails you a notification, then my Y!mail (since it's push enabled) will notify me. Got it! Appreciate your quick responses guys.
(If only iPhone will let you open App links on Safari, but they disabled it sigh where is it)
EDIT: found