It depends :). Once we have information beyond what our eyes can see, as we have now, it is awfully difficult not to make postdictions based on that information.
Four examples of this:
Is the Copernican principle of isotropic and homogeneous distribution of matter true? Could we have predicted this on the basis that the stars are not all clumped in one small region of the sky. Probably. But not definitively.
Could someone with extremely keen eyesight, and under the best seeing conditions available, have deduced by looking at the Magallanic Clouds or the Andromeda Galaxy, that other galaxies existed. Almost certainly not.
Supernovae, which could have told us a lot. I am pretty sure the Chinese royal court astronomers marked them as objects to be watched and pre telescopic European observers recorded them. Again, hindsight is a wonderful thing, but apart from linking them to exploding stars, I am not sure that we could have extrapolated much further on their significance.
Gamma ray sources/bursts would have been noticed, but had a strong source of gamma rays occured "nearby" in the past, this would possibly imply that I would not be writing this now, if you follow me....
Any extrapolations based on those four examples would have faced a barrage of skepticism and, given the times and mindset of the prevailing powers of the pre-telescopic era, a person brave enough to put these ideas forward may have considered themselves lucky merely to have been laughed at.
Source: Herschel's Telescope Based Milky Way Map 1785
Just for comparision to the observations we could make once the telescope was in use, Herschel observed the sky in more than 600 different locations and counted every star he could see to the apparent brightness limit of his telescope. The dark spot near the center is the Sun. This drawing, in my opinion, is genuinely amazing for its day. Putting the Sun near the center may be a holdover from the Ptolemaic idea, or Herschel's genuine belief, I don't know.
Can we infer the existence of dark matter from naked-eye observations? Is it reasonable to say that we can in the sense of if there were no dark matter we wouldn't be here to look at the sky in the first place? Are there any naked-eye clues to the expansion of the universe and dark matter? Would the sky look very different if there were no black holes?
With naked eye astronomy, how far out can we see? Excluding "oddities" such as the Andromeda galaxy and Magellanic clouds, we can see as far as the sixth magnitude stars, (which relates to their luminosity).
Depending on the mass of the black hole, which hopefully would be far, far away, it might affect us. But interstellar dust clouds may have a large part to play in our view of things, as implied in the comments below.
No, we would not see any clue to the cosmological expansion, it is on a different scale entirely. Dark matter would be, as noted in the comments below re dust, would not be noticeable, as far as I know. We only noticed Dark Matter's effects (Zwicky and later Rubin) in the 1930's, and that was in relation to telescopic observations of faraway galaxies.
Two comments, from tfb and Rob Jeffries respectively, just in case they are deleted later:
I think that, based on naked-eye observations only, you might come to the conclusion that the universe was very far from isotropic & homogeneous, because you might work out that the milky way was made of stars, and draw wrong conclusions from that.
Naked eye astronomy is misleading, because it appears to violate the cosmological principle. Even if you exclude the Milky Way, stars brighter than 6th mag are not isotropic.