What is the impact of showing the amount of unattended notifications to the user?
For me it is the inference that the more notifications I have the more value I will have in bothering to click it.

That 1 notification on a social networking site might be a request to play some terrible game.. however 24 notifications are likely to yield at least something beneficial for me to justify having bothered clicking it.

The higher the number the increased urgency I feel to check them (maybe the same person is repeatedly trying to make contact and I am unintentionally ignoring them!).

As for there being a notification with no number, that is easier for me to ignore. In the case of the Windows' PC issues (Action Center) in the task-bar, there is always a notification in it for me, so I have learnt to dismiss it.. I have become de-sensitised to seeing that alert. If however the icon increased in number and I detected this change, then I would deem that to be an increase in urgency and would be more likely to click it again.

I think if I kept clicking Action Center and felt it yielded little value to me then I would be able to filter out if the numbers were to keep increasing, but I would find it more difficult to ignore and feel tricked by it just in-case this new state meant something important this time round..