No. Any external drive (USB or firewire) in my experience is fine when you shut down your Mac without ejecting it.
You only need to eject it before physically disconnecting it from your mac.
The reason I asked is because my SEAGATE!!! 500GB drive decided it would not show up on my desktop last night. So I unplugged it after shutting down, then booted, put USB cable in but it would still not show up. So i lost alot of music and logic projects and had to go get a new one!!!
Really sorry to hear that!
Unfortunately hard drives can and do fail...
Can you still hear the hard drive spinning when it is connected to the power supply?
It may be possible to recover that data from the drive but that might be expensive...
Sometimes a drive won't mount but it doesn't mean that the drive is dead. First thing to try is repairing the disk with Disk Utility (applications / Utilities). If you still can't mount the drive, use a 3rd party disk utility like DiskWarrior[url]http://www.alsoft.com/DiskWarrior/index.html[/url]