Radio signals travel at the speed of light. The galaxy is 100,000 lightyears across. Ergo, it'd take 100,000 years for our signals to reach the otherside of the galaxy. Not "millions." There's also some question as to whether or not our signals can make it much past the influence of our solar system before being blown back by the "wind" in the wide universe beyond our Oort cloud. Further, if our signals will even be distinguishable from the natural radio noise generated by the galaxy itself.