The technical answer is a little messy. Lying to the Notifications API doesn't make the browser itself do anything on the network, but it'll make the site think

The technical answer is a little messy. Lying to the Notifications API doesn't make the browser itself do anything on the network, but it'll make the site think the user has opted into features that require network activity, so you'll incur all the technical costs of the site trying to send you notifications, even though you're not actually seeing the notifications.