Is there a way in PPM Query Builder to search for a date of 'today' such that it uses the date the report is generated, not the date it is defined.
With OOTB features : no.
You have to developp the option by yourself on a custom PortletDefinition+DataSource or a custom Report.
Yes ! We are in 2016 and PPM is still not able to manage "Today" / "This week" / "This month" in common validations (Request Search / Portlet FIlters).