As far as Time Machine backups go - as long as the Mac can see the disk and it's got enough space then it doesn't matter what sort of drive it is. I agree with you regarding the convenience of the disk just being
there on your network and not having to plug it in to the Mac.
Check the router documentation. Mine has usb for connecting disks but it only supports FAT16 or FAT32 and I think there's a size limitation too. If you were sold both together and told they could be used in this manner then one would hope they'd work, but if they don't you'd have a case for getting your money back.
Also - check that you're connecting to right USB port on the router. Some routers have USB ports for wireless dongles as a backup for if the landline fails. Similarly, some slots are for printers only (like the USB port on the Apple Airport Expresses).