Yes & no.
There is power flowing through the IDE cable for signalling, but it's not powering the devices motors, so it will only be small currents, and it's unlikely that you will damage the device.
But at the same time, you have the motherboard supplying the device, and simply unplugging it while the pC is on can cause a voltage spike on the ide chain, which can damage the motherboard, or other device attached to the IDE chain.
Either way. Don't do it. Turn the damn PC off before disconnecting your devices.