You can turn notifications off on the job, but they do need to dispatch to add the notes. If you turn notifications off before they do that, the customer shouldn't get a notification.
New to this not sure if this would help. You could Send them A TASK in the TASK Manager to review the Existing Job and Update the Job Summary to add notes or the Invoice summary. That way it wouldnt be a Dispatched Job Just Updating the last One with the New Info.