do you mean somehow executing a script on the page of saved search results when the user views it, to trigger some action or give them a popup or whatever? if so, no, the search results (or search creation) page is not scriptable

That would be one approach I was referring to. But I also was trying to determine if the data that is being used to generate the Saved Search could be manipulated in something like a User Script and new columns could be added or data modified before it was displayed.