I managed to get it woking on Mavericks 10.9.1, on AMD, but there's one catch. You need an existing Intel Hackintosh, or, like me, a real Mac. This may not help you, but hopefully somebody out there will benefit from it.
I created a new account on my MBA, and set up my iCloud account, completing one sync. Now the idea is to transfer this account using migration assistant. Theoretically this should be possible provided both computers are on the same network, and the transfer occurs over the network. This didn't work for me however, and I resorted to using a Time Machine backup of my MBA and used Migration Assistant on my AMD PC to transfer only the account from the Time Machine backup. Once complete, the account already had all of the iCloud settings, and seems to still be syncing successfully. iMessage doesn't work, but that's the only thing. I wouldn't advise touching the iCloud Account Settings pane in system preferences though, not sure quite what would happen.
Not exactly the easiest and most convenient method to do it, but it appears to be the only way at the moment. Hopefully a kernel for AMD that allows iCloud will be released shortly.