If I encrypt a Time Machine backup disk, is the entire disk encrypted or just the Backups.backupdb directory?

It encrypts the partition that you use for Time Machine, which likely means the entire disk. If you partition the drive the other partitions will not be encrypted and should mount (I have not tested this).

You can see that "Time Machine" is encrypted, but "Other Backups" is not.

The quick answer is the whole disk is "encrypted".

This isn't technically true since you could conceivably use Disk Utility in debug mode / diskutil on the command line to partition the Drobo volume to have several partitions.

In practice - Time Machine just is working on a partition within a volume, so the idea of the "whole disk" is in reference to the consumer perception where a "disk" is connected and the icon for that "disk" shows up even though the implementation of a "disk" is a partition that contains encrypted data and relies on CoreStorage to do the encryption/decryption before the file system can be mounted on OS X.

It is actually the entire partition that is encrypted so if only one partition then in effect the entire disk. So other OSs can't read that partition.

If you want them to, partition the disk and encrypt only the part containing the backups.