Yes, it is a thing. It helps pinpoint dates of events that occurred in relation to various astronomical events, for one application.

Another is gathering data about stellar phenomena. Sirius was once described as red, now it's white.

And of course, there's the historical application—how cultures observe and interpret astronomical phenomena gives us insight into their social and religious concerns.

Edit: hit submit too soon

Interestingly enough, Carl Sagan was the crackpot who first seriously suggested archaeo-astronomical research into ancient aliens: "Direct Contact Among Galactic Civilizations by Relativistic Time Dilation" Planetary Space Science (1963) [PDF]. He argued that the Sumerian myth of the Apkallu could potentially record contact with an intervening series of extraterrestrial visitors, similar to how myths among the Tlingit recorded contact with Europeans. Later this notion would be popularized and rendered ridiculous by von Daniken's terrible Chariots of the Gods. Which is unfortunate because I would be very interested in reading a rigorous study into the questions Sagan outlined. Looking for evidence of ETIs in the historical record makes at least as much sense as looking for evidence of ETIs in radio signals.