I've tested this on Firewire and eSATA drives (well, the same drive but using those 2 different connectors), and the behavior on my Seagate drive is to simply unmount the drive, causing the external drive to behave as if the data cable had been disconnected—the HDD's light begins to dim and then turns off.
However, the drive itself doesn't actually turn off, even though it may appear to be (no spinning, no sound, no lights). This is so that the standard re-mounting procedure in Windows (disconnecting and reconnecting the Firewire/eSATA cable) will allow the drive to be re-mounted.
I believe the procedure on Macs is slightly different, and you can just re-mount it in software. (You can probably do the same thing in Windows 7 by disabling/re-enabling the USB/FireWire/SATA device in Device Manager, but it's kind of a pain.) But this too would require that the drive doesn't get shut off when you eject the disk.
As a side note, many external HDDs, such as mine, do not have a power switch. The only way to actually turn off its power is to disconnect the power cable. And the way to turn it on is to simply plug the power cable in. Otherwise, the HDD just goes into standby or sleep mode.