Yup, they do.
The "add features to Windows" shortcut is actually in the control panel for Win 8.1. Once you add Media Center, the shortcut disappears, so clearly that was the only feature MS had in mind for that shortcut.
Yes, they work just fine. Although, for my situation, I installed using my original Win8 key then upgraded to the Media Center after and didn't use the key to actually install the OS (yea, I used the leaked way).