There are surely a lot of variations and possibilities of how to achieve your aim.
If a static OVERLAY do fit your needs, why not. → Just place a transparent PNG-file over your map and set it as hidden.
For example on a button-click you then unhide/show your OVERLAY-BOUNDARIES → that’s it. Of course this would be just an STATIC solution, like you already mentioned.
To generate a more automatic fitting overlay-functionality, you would need an HTML-Component or a Custom-Element + and a lot of CODING.
In case of a static solution, you even perhaps should use a → MULTI-STATE-BOX, this way it would even be possible to do different kinds of OVERLAYING.