Is it possible to set-up the app manifest in such way, that when a condition is met, the side pane of an add-in opens automatically when the object is opened?
Office.js Add-ins are designed to be invoked by end user. You cannot open task pane by using manifest or JS. So the answer on your question is no, you cannot open task pane automatically based on condition met.
Possible work around (not the solution to your question through) would be to implement a pinnable taskpane in Outlook. This would gives to your user choice to keep your add-in open all the time when navigating from one appointment to another, but still depend on user choice to keep the pane open. Please read more about Implement a pinnable taskpane in Outlook and the announcement in the MSDN blog
I.e. when the user opens an event in Outlook calendar, and the event has some text in the description, the add-in pane is opened each time the user opens the event form?
This has work around as well. You may have rules in the manifest file, when your add-in will be available (not invoked, but available to user). Still user choice to click on the add-in or not. Please see Activation rules for Outlook add-ins for more information.
Update:
Thanks to @EduardoCMB comment, the feature is now available for Word, Excel and PowerPoint. There are list of "best practices" on when and how to use the feature. Please refer to the documentation ... Automatically open a task pane with a document