Dont be skeptic, it is possible with the aforementioned hardware. You can expect two basic issues for any implementation:
1. Speed or MIPS required
2. Memory required

I reckon, if my memory is right, CC2420 could work with 250kHz SPI clock, so your whatsoever '51 variant should be capable.

Memory could be the burning issue when working with stack based protocols. It once again boils down to what functions of Zigbee you would like to implement.

Full function device capability node: I doubt with the amount of RAM available. I went through the specs of DS89C450, and it is impressive regarding flash and MIPS. But rethink the implementation functions since the RAM available is 1kB.

Now tell us, what exactly the application is for which you would like to use Zigbee? If it is a "fixed number of nodes" application, as I've already mentioned, you could very well use any Zigbee PHY chip as a RF transceiver.

Remember, most of the RAM requirement for the stack is for "inter-operability" across Zigbee devices, and for the network discovery and routing protocols.

I missed answering "Xbee". It is similar to CC2420 except instead of SPI, you could use UART for the interface with your favorite '51 variant and the radio chip.