UPDATE: No way to do so via LotusScript alone, but perhaps you can get this information via the Lotus Notes C API.

The NSFDbGetUserActivity method will either return the user activity information (shown in that dialog) or it will return ERR_SPECIAL_ID if there is no summary information. This is not a precise way to determine whether the record activity flag is checked, but you could infer the state of the flag from the result of the method.

Of course, there’s still the chance the flag is checked, but no activity has been recorded yet, or conversely the flag is not checked but activity was previously recorded in the database.

Another solution may be to programmatically perform an action that would normally get recorded in the User Activity. You could then check to see if that activity is in fact recorded, and you’d then know whether that flag was active or not. If you dedicate a special Notes user to run this code, it would be easier to pick out that user from the list of activities avoiding a false positive caused by some normal end-user activity.

The code below shows you how to get at the User Activity information via the C API, taken from example #3 on this tutorial page: http://www.triplewhitefox.com/tech-calling-c-api-from-lotusscript