Possibly. The theory here is to use a shared variable that flags for suppression or not. However the variable has to reside on the report canvas above the section that you want to suppress in order to use it. So your problem becomes getting the variable to be before the group header. Perhaps you can create a GHa,b and c.
A is the subreport location, B is the shared variable location and C is Group Name display location that can be suppressed or shown based on the value in GHb?
I think that might work but have not tested it out. You can also search this site for more tips on this as I know similar questions have been addressed.