No external notification is planned for the first iteration. By setting an expiration time far enough in time, you can ensure that other signers will have time to sign it.
When it's ready we'll hook it up to Keychain so it will be live every time the browser is opened basically.
It's a good idea though and could be added as an optional parameter during login at a later stage.
Going to have a think about this and how it fits in with Podping because we are slowly working on a mobile friendly notification subscription system for Podpings and I think it might work nicely for this.