Depends on how much the Z-80 is doing. You can go the C-64/Atari way where the filesystem is running on the disk drive and the main CPU just runs the applications.
On Atari 8-bits, the filesystem ran on the computer itself. There was an MOS 6507 processor in the drive, but that was for communicating on the SIO bus.
Fascinating. I wonder if one could fit a filesystem in the floppy ROM - this would free up memory in the host computer for other operations, and allow extended functionality in the filesystem that's absent from existing implementations.