Will it be possible to store a graph as a percolate query?
Not directly but it should be easy to implement. Another feature coming in 5.0 is the ability to configure "drill-down urls". These allow selections in the graph workspace to be passed as parameters to other URLs e.g. Kibana visualizations or 3rd party websites. Here's how it is configured in the new UI:
Once configured you have a button that allows users to click to perform that action on a selection.
If you can provide a simple web app that takes the parameters passed in the URL it could make a call to save them as a percolator query (perhaps pausing first to ask the user to configure a choice of tag e.g. "death metal"). We haven't added such a percolator-saving function as yet but it would be easy to implement.
For the existing 2.4 release, there is a more manual set of steps you can follow to get hold of what would be your classifier query which I have documented here: https://www.youtube.com/watch?v=1zLcQF5luDE