No, there is a background process still running. You will need to scroll down a bit further in the Task Manager. I understand that this is what Windows is ignoring when it shuts down.
The workaround during version 7 was to close eM Client a few seconds before shut down of Windows.
I remember it was much discussed at the time, and then some changes were made to improve the way eM Client shut down. As far as I am aware it is less of a problem with version 8 users than it was with 7. It is interesting Ian that you said you didn’t have this issue with version 7.
I think you will wait a lot longer, but one thing you can do while you wait is to make sure that you keep eM Client up to date by checking the Release History regularly. There is already a newer version there than what you are using, and a link for an even newer unreleased version was given recently in this post: