Moved this from the Report Center to Report Requests & Questions. Please note that the Report Center is for posting finished reports, not questions.
In regards to your question: we don't specifically scan for this information. If there is a related error or warning in the Event Viewer when a mailbox is almost full, you could build an event log report for this. A sample report was posted
here. Keep in mind that only errors are scanned by default. Additional event types can be enabled for scanning by following
these instructions.