Conceptually it should be the same as an flash memory USB drive, the linux kernel should detect it but mounting the partitions is usually left to the user. I have a Asus 52x CDRW drive (I admit it is not a HD, but it shouldn't matter to the kernel) that is normally a "in the case" drive. It is mounted in a USB 2.0 & Firewire portable case & I have burned CDRs in both Win2k & Knoppix over usb2.0 without any issues.

Of the "Hard drive in a portable case" devices that I have seen, practically all of them work with Linux. Some of those drives (example) work with Linux but the "1 touch backup" feature of the device is just a windows only program that performs the backup. So if you buy the drive for that feature, then yes, that feature will not work with Linux.

I hope this helps.
James