Easiest way to do this is to add AVG(dummy) also to columns shelf. This will give you a scatter plot but you can still have your donut chart as a single mark in the middle of it. Hide headers for pills on both shelves so you don't see axis. Set it to fill entire view and increase the size of the donut by adjusting the size slider.
Then you can do two things 1) Use a background image 2) Put this in a dashboard as a floating object and put the image you want to show as another floating object but below it in Z-order
If you do 1 when pie chart disappears the background image will be visible.
If you do 2, when everything is filtered out from the sheet, you will see that the whole floating sheet object disappears exposing the image underneath in the dashboard.
It works perfectly.
Thanks a lot!