Can a 2006 Mac Pro that can't go above Snow Leopard physically on the host run Mavericks with vmware Fusion virtually?
I'm guessing you can, and here's why (from VirtualBox):
VirtualBox supports 64-bit guest operating systems, even on 32-bit host operating systems provided that the following conditions are met:
You need a 64-bit processor with hardware virtualization support (see Section 10.3, “Hardware vs. software virtualization”).
You must enable hardware virtualization for the particular VM for which you want 64-bit support; software virtualization is not supported for 64-bit VMs.
If you want to use 64-bit guest support on a 32-bit host operating system, you must also select a 64-bit operating system for the particular VM. Since supporting 64 bits on 32-bit hosts incurs additional overhead, VirtualBox only enables this support upon explicit request.
VMWare Fusion says something similar (search the FAQ for "64-bit").
Assuming your Mac Pro is the 2.66 Quad Core, EveryMac confirms that your processor is 64-bit. Give it a try, hit the forums, and good luck!