Hey Mate,
The One is basically just a 'Host' if you will. It is programmed off other remotes (mine off my old DualDigital TV card remote).
Probably the best way to do what you're looking for is to program the remote from your MCE remote and use a third party software like Girder or HIP to recognise the IR command and translate it to keyboard commands.
So yes, it is possible to use it as a keyboard, in a sense.
Mouse as in pointing device, I wouldn't imagine so but the logitech forums should help you out there.
I use HIP to capture the PCOff command from my One and translate it to the keyboard command to shutdown the PC to Standby - just like the MCE remote does natively. Of course, this is only one example and the MCE remote that JRiver sells does this without the need for HIP, but this works for me.