this should be a little bit tricky. the "link" function for PI webparts between PI TreeView and PI Graphic is provided by MS Sharepoint server actually. Therefore, if needs to achieve your goal, modifying the sharepoint server configuration should be necessary. I will check on the internet if there has the solution.
To achieve what you want you'll have to create a "man-in-the-middle" webpart. This will be a webpart without any GUI, which would need to implement the IParametersOutConsumer and IParametersOutProvider interfaces in order to communicate with the PI Webparts. You can then communicate with the PI Webparts client side, without the need to refresh the page every time a new selection is done.
Another, much simpler solution could be to just set the Chrome Type of the PI Graphics webpart to 'None'. This way the only thing visible in the webpart would be a small text saying "No Data Configured". You could also try experimenting with creating a default SVG file which contains nothing, by showing that it would appear that the webpage is empty where the PI Graphic webpart is placed.
I see there is a setting in the PI Graphic webpart where it takes an XSL file. Since XSL is a powerful programming language I suppose you could determine if the reference is valid there, and then output the default, empty SVG if not valid.