After further contemplation, I'm inclined to think that it may take less than 200 years for a technological civilization to go from the advancement of electromagnetic communication to the advent of strong AI. Even if it takes 1000 years, it's still an insignificantly short period of time compared to the almost one billion years it took for the first life to form on Earth.

Since a technological civilization will presumably want as much intelligence and computational capacity as possible (to find out one's purpose here, or perhaps to play god by simulating a universe that is as realistic as possible), it seems likely that it billow out like a cloud of nano-, pico- or femtoscale von Neumann machines in all directions at close to the speed of light. This will probably happen within a few minutes after the strong AI is started the first time, since it will recursively make itself more intelligent. Its purpose may likely be to convert the planets, stars and galaxies into intelligent matter. Ideally, every planck volume in the universe will somehow be arranged into a component of its universal computer. Perhaps it will even try to stop the expansion of the universe to invoke the Omega Point to attain the only true immortality and omnipotence there is.

In other words, why would the aliens want to talk to us when they can just breeze by us like a dark .999c wind on a rainy Sunday morning, retool our atoms into a computer and fulfil their own digital dreams instead?