There is a claim that habitable-zone orbits are stable around both components of the Alpha Centauri binary, and at least one planet has been detected (though not in the habitable zone). Both stars appear to be about as old as the Sun or older. There is now some serious effort to look for an "Earth Proxima" (Mission Centaur) in the Alpha Centauri system. Seems like a lot more to go on than SETI has had with other places they've been listening to. With that in mind, has there ever been any effort to listen for artificial signals from Alpha Centauri or to send something like an "Arecibo message"?
Since Alpha Centauri is only about 4 light years away, it would be reasonable to expect that if there is an intelligence present with the means and desire to listen and reply (admittedly a whole lot of "ifs"), we shouldn't have to wait more than 10 years to get a result if one is at all forthcoming, and it would be a relatively inexpensive exercise to undertake, even if nothing comes of it.