Jeff,
It will show up on the LinkStation as a share 'usbdisk1'.
I just verified that using a Windows PC, I could access \\linkstation\usbdisk1 and both read and write to it from the Windows PC.
Thus, you could run a Windows PC software backup program and backup to the USB Disk as long as that backup software program allows backing up to a network share (\\linkstation\usbdisk1).
The data will move through the LinkStation and onto the USB Drive, it will not be on the LinkStation's internal drive.
The LinkStation can write to the FAT32 drive as well so I'm not sure I understand the "even if the LS can't write to it" part.