Science can't answer that with empirical certainty. Experienced fishermen, however, can answer with relative certainty. (We don't need absolutes; "close enough" is fine.) Bluegills can see plankton that are, to us, microscopic. Of this we have conclusive, empirical proof. So, of course—logic demands bluegills can see well enough to see fishing line. But do they care about the line?
You can catch bluegills on 10-pound test mono in clear water sometimes (I wouldn't recommend it, unless the bluegills weigh over a pound and they’re in tight, heavy cover). Walleyes do not have the visual acuity of bluegills, nor do they need it. Their prey is always larger than a zooplankton. Their eyes may not be able to focus on things quite as small, but they can see quite well and in color, including ultraviolet (which you cannot see). The rods and cones in their eyes are particularly sensitive to the green part of the spectrum, which could be why chartreuse is such a good color for walleyes in stained and murky waters. If the line is chartreuse, walleyes see it easier. When we use clear fluorocarbon, can walleyes see it? Yes, but with much more difficulty. Fluorocarbon breaks up and disappears for a few feet here and there, and fish often can’t see the connection between lure and line. Fish have the visual acuity to see line, but do they care about it? Especially when focused on a lure, the fact that the line is visible does not mean it registers as a threat. Nevertheless, I've watched steelhead disappear in a hurry when 6-pound clear or green monofilament passed over their heads in clear water. On those occasions, the lure was far away and out of sight. But I've caught a lot of steelhead on 12-pound mono pitching cranks, spoons, and spinners in very clear rivers. They don’t spook from the line in that instance because they focus on the flashy, noisy thing. They can certainly see 12 pound, but, when aggressive, and a flashy-noisy thing goes by, they may see the line without actually taking note of it. All of their focus is bent on the lure. Which suggests that, the more aggressive the lure, the less you should be concerned about the visibility of the line. Conversely, the less aggressive the presentation, the more attention you might want to devote to hiding the line.
But the fact that steelhead in clear water can be caught on 12-pound line reveals nothing about the attitudes of all the fish that flashed behind the lure and failed to bite. So I want to hide the line as much as I can in almost any situation. My theory is that fish take in more data than they use, just as we do. But as we pressure them, more of that data starts to creep into their awareness, especially when attached to life-threatening events.