Hide the header of a view block when there is no content
Well I think you are asking how to hide a block view completely when it is inserted as a global: view area in the header of another view.


  For the parent view:


When inserting the block view into the header of another view, make sure you leave the box unchecked that says: Display even if view has no result




  For the block view that is being inserted check these 3 things:


1:
If you are displaying fields in the block view, you want first make sure you are hiding any empty fields under Show: Fields | Settings 



2:
Then you want make sure you you have the Hide block if the view output is empty: set to yes under the advanced tab in the block view.



3:
You also want to add a contextual filter for the block view that defines the context you want. Then set the WHEN THE FILTER VALUE IS NOT AVAILABLE setting to hide view. (For the image below, my context needed was taxonomy term ID.)



Hope this helps!