Hi Michelle

There is an existing feature TL-9269 to add a permission to create a scheduled report - a role with this permission prevented wouldn't be able to create a scheduled report. This is a bit different than what you are asking about but it has the same effect. 

The scheduled report used to automatically be sent to yourself - but now this needs to be explicitly done. There is also a feature request TL-8783 The Author of a scheduled report should have clear option to be included in emailed report.

regards