Microsoft Outlook 2016 for Mac and Outlook for Mac 2011 does not update your Microsoft Exchange calendar when you accept a meeting request without sending a response.
When you accept a meeting and then select Do not Send a Response, Outlook for Mac updates your local calendar with the acceptance only, it does not update the acceptance on your Exchange mailbox. However, the meeting is marked as Busy on the Exchange calendar.
To resolve this issue, use the Respond with Comments option or the Respond without Comments option when you accept a meeting. Either of these options will update the acceptance on Exchange. Then, your acceptance can be synched with other devices that are connected to your Exchange calendar.
When you select Do not Send a Response when you accept a meeting request, Outlook updates only the local calendar with your acceptance. No other calendars are updated. This includes your calendar on your Exchange mailbox. Therefore, the meeting acceptance is not visible on Outlook Web App (OWA) or on any device that is synching from the Exchange server. Also, the meeting orgainizer is not notified that you have accepted the meeting.