They can see ALL lines in clear to semi-clear water, but the depth and clarity of water you're fishing in can "hide" the color of the line.
I use (or have used) hi-vis line, red line, green line (high & low vis), clear/blue line, & hi-vis braid ... sometimes alone & sometimes in combination ... and have caught fish on them all. And in most cases I have tied the line directly to the bait/hook. The waters I fish are lightly stained to moderately stained (1-3ft visibility depth). I've used the "colored" lines so that I can see them, regardless of whether the fish can or not. I don't believe the fish are as interested in the line color as much as they are what's on the end of it. I'm not even sure they can comprehend what "line" is, or that they are ever actually "line shy". But, that's just my opinion.