On my tool bar, I don't get any indication I have emails until I actually open email and then the number icon shows telling me I have emails. What's the point?
IMAC (RETINA 5K, 27-INCH, LATE 2015), iOS 11, OS Sierra
When a mail arrives in inbox , and you only open mail application and don't read or click on the mail it shows as red dot over the mail application .To remove the red color dot you gave to click on the that mail .
And a blue dot is shown over the mail in inbox .
And if you open system preferences > notification centre and select the mail and choose as none .
And also turn on do not disturb set the desired selected timings the mail notification that comes on top right corner of desktop will stop .
Notification centre configuration is confined , it ups to you stop notifications on the desktop and viewing mail is a different , because mail application is totally different than notification centre .
Apple mail application has its own rules and its just a configuration with web mail account , there are options for read mails in server account see this gmail article Change email notifications - iPhone & iPad - Gmail Help
And read this article for notification center macOS Sierra: Receive or stop notifications
