If I remember correctly it actually depends on if the system is in standby or not. If you plug in a Wii it starts off with no power (red light) so Wii Remotes won't turn it on. Once you turn it on however, turning it off kicks it into standby mode (yellow light), where paired Wiimotes will turn it on.

I can't verify this with my Wii right now because it's standby behavior is... strange. I don't know if it's because I have bootmii/boot2 on it or what, but when it's supposed to be in standby, it instead constantly runs the fan as if it were still on. At some point in the past it worked as I described above though.