The thin gas in the galaxy - what we call the "interstellar medium" - does scatter and disperse photons. This effect is small at high frequencies (like visible light), but increases as you go down to lower frequencies (radio waves etc). But even in radio waves, we're still limited more by the resolution of our telescopes than the fuzziness causes by the galaxy's "atmosphere" - although the Event Horizon Telescope is awfully close to the point where that matters.

What we do see is that radio waves of different frequencies take a different time to reach us, and will be a little out of phase. So if some event happens that emits radio waves are a broad range of frequencies, we don't get receive that emission at once. Instead, the higher frequency radio waves arrive first, and the low frequency waves arrive later. Instead of a single broad pulse, what we get is like a quick glissando from high pitch to low pitch.

You can actually use this to measure the thickness of the interstellar medium. The slower the slide in pitch is, the more material was along the path of the radio wave. So if you already know the source and the distance to the source, you now know the "column density" of interstellar stuff between Earth and the source. Do that with a bunch of sources and you start to build a map of the density of stuff in the galaxy, which can be used to complement other measures for the interstellar medium.