Circles are not always invisible. A circle made up by a closed-loop line source of photons would be visible. (They're kind of hard to make, though.)
It's sort of the question of what is the smallest thing a human can "see". Stars, for example, are extremely small, far below the resolution of the human eye (outside of the atmosphere, of course). Yet seeing them is not a problem, you just get an unresolved image.
Visible means "able to be seen." You can see things that emit or reflect light. Abstract concepts don't emit or reflect light.
Real objects can only approximate a circle. The pedantic definition of a circle in this context is being used to make the point that you can't make a perfect circle with pixels.
No. If you made an abstract object that emitted light, like the "linear light source" I hypothesized, it would be a perfect circle, and visible. It doesn't exist, of course, but if it did, it would be visible... ;-)
It's sort of the question of what is the smallest thing a human can "see". Stars, for example, are extremely small, far below the resolution of the human eye (outside of the atmosphere, of course). Yet seeing them is not a problem, you just get an unresolved image.