I'd say it's possible for us to send at least a flyby probe to Alpha Centauri, but that the amount of scientific return for that investment is perhaps too small to be worth it. I have some ideas for methods to accomplish this with mostly existing technology, but there's no getting around a very large amount of mass that must be launched into space (a large and heavy X-ray laser).

A much lower investment of launch mass in the form of large "eyeglass" or "loopglass" space telescopes could provide much the same scientific return, without even waiting for probes to trek across interstellar space for many years.