Is it possible for the notification icon to remain until one has selected the unread email, like Outlook does?
No. See the reply from Paul at eM Client support on the following thread.
email notification kept until read - Mail - eM Client
The notification is used to indicate there’s new mail available in the application, once you open the application it is considered you’re aware of this and you still see the indication of unread email inside the application.
Thank you,
Paul.