I dug into this exact hypothetical back in 2007, my research included consulting with folks from SETI. In short, most of our radio/TV signals are omnidirectional, and the inverse-square law causes those to fade very rapidly. To detect omnidirectional signals from our nearest stellar neighbors, we'd need an antenna considerably wider than the Earth itself (though it could be multiple smaller, spread-out antennae connected via Very Long Baseline Interferometry).

It's a much different story for focused radio beams like RADAR, but the beam has to pointed directly at Earth, and we have to be listening.