Yes, what call "the speed of light" applies to all forms of electro-magnetic radiation which includes visible light and radio (and infra red, ultra violet, X-ray, microwave radiation etc). All these have the same velocity in a vacuum, so radio astronomy is looking into past in the same way as ordinary, visible light astronomy.
One difference though is in the size of intruments used. The sensitivity to E-M waves receives varies inversely to the wavelength. As radiowaves are much longer than light waves, larger receivers are needed for the same degree of resolution. This is why large arrays of seperate instruments are used for radio astronomy, the signals received being combined.
Some forms of E-M radiation mentioned above are of wavelengths that cannot penetrate tthe earth's atmosphere, so ground based observations are not possible.