correct. The signal wire is only used to tell the antenna to go up or down based on the presence or absence of a voltage. The power draw from the motor comes through the constant power source, otherwise when you shut off the car (or radio, or other source of power) the antenna would not be able to complete its cycle.

It's a little different than the technology used by the factory, and more than a bit more convenient. That particular antenna draws very little power and should not overheat any circuit. And of course it only draws when going up and down...

The circuit is completed by the mounting/ground strap that screws to the trunk floor. It also serves as an anti-torque bracket.

Does the body harness in a coupe have any extra, unused wiring connectors such as rear defogger? If so, you can find the other end, and tap the fuse box power into the existing body wire just to get it to the antenna. Just be sure you're looking at the same wire at both ends