Do Solid State Drives need Power Management? Do they need sleep? Is there any positive (or negative) to checking the power management option "Put hard disks to sleep" when I only have a SSD drive installed?

Is there any difference if I'm connected to another external drive, or Mac in Firewire taget mode?
There is no advantage or effect on SSDs with the "Put hard disk to sleep". This setting enabled a spinning disk to spin-down while not in use. With no mechanical moving parts, there is no effect on an SSD. 

Externally connected mechanical drives will still adhere to the setting.

See Apple Support page: OS X: Saving energy with Sleep