This is not difficult, although it will suppress the section completely when viewing AND exporting - there is no way to suppress for just export.
1. On the section where the subreport is located, in the Section Expert turn on "Suppress Blank Section".
2. For each section in the subreport, set the suppression formula for each section to something like:
IsNull({table.Some Key Field})
This will suppress all of the sections in the subreport if there is no data and the section in the main report will suppress because its contents are blank.
-Dell