There are already notifications that you get on the "StackExchange" popup. When there is a new comment, or a new answer for your question, a number appears to the right side of that popup.
To notice that those notifications are passed along the network of sites; for example, if I have a comment on an answer I gave on Meta Stack Overflow, and I am reading a question on Stack Overflow, or Drupal Answers, I would get notified the same; I would not need to be on Meta Stack Overflow to get my notifications.
If you are getting those notifications via email is probably because you set them to be received via email.
Normally, those notifications are not given through via email, and new comments/answers directed to you are reported in the Super Drop-down Menu®.
If you are suggesting a notification on the top bar saying that you have X new comments (or X new answers), that is already done with the number that appears close to the Super Drop-down Menu®. If you are suggesting a notification on the top bar for each new comment (or answer), that would be not practice, as you could get many notifications (even higher than 10, depending on how much frequently you visit the SE sites where you have an account). Supposing that the notifications would appear all in the same instant, they could become a wall; if they appear one after the other, they would be less practical than the actual notifications.
If I have to choose between the actual notification system, and the one you propose, I prefer the actual system. Clearly, both the notifications could not co-exist, and having both of them would be a not necessary duplication of code.