I am wondering if I can use web push notifications to update a web page without displaying a notification for the user to interact with. Essentially I want to refresh data after an event on the server.
If this is possible, is it still necessary to receive permission from the user to send these push updates?
Yes, you can send push messages without showing a notification, but there are limitations on both Firefox and Chrome on the raw number of "invisible" push messages and the rate at which you send them.
You can experiment a bit with the quotas in different browers using the Push Quota ServiceWorker Cookbook example.