Thanks for the replies. With the AnywhereUSB connected to a virtual machine I tried connecting various flash drives and a USB mouse, with results as described in my original post.
I tried connecting to a physical machine on the network with a new set of issues. On the physical machine (Windows 7, 64), the configuration utility sees the AnywhereUSB and says, "connecting to this host pc" with a driver status of "can not find remote hub at xxx.xxx.xxx.xxx". Lights on the USB ports of the device are dark, and a restart of the OS and reboot fo the Digi device don't result in a successful connection.
Over the next few days I'll throw more testing at it, I'm still optimistic this will be usable on our network.