aakk9999 - 9:40 pm on Jul 10, 2013 (gmt 0)
To answer your questions:
Yes, if two URLs display the same page content, then this is viewed as duplicate content.
Q: would these be viewed as duplicate content?
If you specify the exact URL to be removed, then only this URL is removed (unless the specified URL is a folder, and you click on "Remove directory"). If you go this route, then the URL to be removed must either return 404/410 or be blocked by robots.txt. However, I would also read this before you proceed with URL removal: [support.google.com...]
Q: would removing them using the Remove URL tool kill the site entirely?
There is also another way of addressing duplicate content issue, which is to use canonical link element on the home page, but before doing this it would be a good idea to figure out whether incorrect URLs are somehow created from within your client's site.