Hello!
No, I re-checked, and it still doesn't remove the notification icon until I open Aqua Mail.
I have checked, and there are no unread emails in any account (and Aqua Mail displays no number to indicate that (it does display the number at other times, so I know that works!)).
My test right now was:
1) Make sure that no email is unread in Aqua Mail.
2) Send an email to myself using Outlook. (subject = "test")
3) Press the circular arrow in the aqua mail widget to instantly check for new messages.
4) Notice that the mail appears in the Aqua Mail widget and that there is a notification icon. When pulling down the notification bar I can see that it displays the correct subject there as well (subject = "test").
5) Read the email in Outlook and make sure that it is marked read there.
6) Press the circular arrow in the aqua mail widget to instantly check for new messages.
7) Notice that the email is no longer highlighted in the Aqua Mail widget. (correct)

Notice that the notification icon is still present (incorrect).
9) When pulling down the notification bar I can see that it displays the subject of the email that now should be read (subject = "test")
Is there some setting that I have set incorrectly?
I have checked "Only when new messages", "Only when there are changes", and I have chosen "Notify About / All unread messages"