I don't know about such powerbars in particular, but older devices specifically designed to do this usually were not sensitive enough to detect the difference between a line level device (i.e. no power amp inside) being on and being off.

There's very little difference between the amount of current drawn by "vampire power," i.e. the power needed to have the unit in standby, with the IR receiving circuitry powered up, and "ON," where the rest of the circuitry is active. This was especially true with old 480i cable boxes that put out a black video signal when "off."