Despite the apparent combination of options on the Queue's edit page, there are only three options available: notify members of the queue, notify an arbitrary email address, and notify members of the queue and an arbitrary email address. The Send Email to Members checkbox only has an effect when Queue Email is not blank. See How to stop email notification to Queue members?.
So, if you want to completely suppress notifications for a queue, you need to use a non-existent address (try [email protected]) and set Send Email to Members to False/Unchecked. Using a non-existent address is also mentioned in the link from above:
Although this is standard functionality, you can put in a "dummy" email address for the Queue email. This way, you can still keep the preference to send an email to the Queue in place, while not automatically sending an email to all Queue members.