Actually, the role of the Availability settings is exactly that of preventing unwanted interruptions.
If people set their status to Busy, it means that they are working on something, or that they are on the phone with someone, and cannot receive notifications.
All notifications are delivered and do not get lost, irrespective of the busy status of a team member. The notifications are collected in the Notifications tab/ Messages tab up until the moment when it is convenient for the recipient to read them.
You can, however, push a message to someone who has set a busy status, by using this symbol: