You can certainly do that with some customization.
What I would do is use the builder to create the Main Stage action then keep the data-storymaps="MJ-ACTION-1470675977260" on the element that you want to trigger the action on hover. Then you can just remove the link.
After you catch the hover event using jQuery for example (https://api.jquery.com/hover/), you will just have to do something like this
$.each(app.data.getContentActions(), function(i, action){
if (action.id == "the id of the element hovered") {
performAction(action);
}
});
When navigating away from the element if you want to restore the state of the Main Stage, in some case something as simple as below will works.
topic.publish("story-perform-action-media", app.data.getCurrentSection().media);
But that won't work if you are re configuring the same map (like showing a different layer), for that you would need to copy most of the logic from map-journal-storytelling-template-js/StoryText.js at master · Esri/map-journal-storytelling-template....