I don't think you need extra hardware with the Elite. You just need to read the manual carefully and understand the activity based Harmony process.
You do need to set MC to accept commands from both an IR and Keyboard device. Tools/Options/Remote Control/Device & Options/Select Input Devices/ then select "Microsoft MCE" and "Remote, keyboard, gamepad, or other HID". Both should show as active.
With my old Harmony 880 there is a bit of an issue even with those settings in that MC does not seem to be able to learn some keyboard commands, so even though my Harmony can send some Windows keyboard combinations, MC won't receive them. Plus a lot of the commands conflict with standard Windows keyboard combinations, so I can't use them for other actions. Like Win+1 to 9 for example, starts the program on the task bar x positions from the left.
If you set up the Elite through the Harmony site, you should be able to find a list of commands used by the Elite there, and even reprogram what it sends.
Anyway, I don't have an Elite so can't help specifically, without reading the manual. But it uses a hub that I assume receives the Bluetooth commands, and probably resends them to your devices as IR commands, if you set it up that way, or sends them to the PC using a USB connection. Something along those lines.