Sure.  After all, the chumby supports the iPod, many models of which use hard drives.  It really doesn't know (or care about) the difference between a USB flash drive and a USB hard drive since they're both USB storage devices.

The current restriction is that the drive be formatted in a filesystem the chumby understands, typically FAT32 or HFS+ - that means no NTFS, ext3, etc unless you add a kernel module.