Is the first image of a black hole that was captured by the Event Horizon Telescope what would be seen with a large enough optical telescope (or with the naked eye from a proper distance of the black hole)? If so, how do radio telescopes gather information about visible light?
How do radio telescopes gather information about visible light?
They don't; the picture you saw all over the news was a false color image, where frequencies are shifted from the radio spectrum to the visible spectrum (blue meaning shorter radio wavelengths and red meaning longer radio wavelengths) and/or the intensities mapped to different colors (instead of just affecting the brightness as with true color images).
Or, to quote an old StarChild question:
The term "false color" is used to describe what astronomers (and others) often do to images to make them more comprehensible. Long ago, when radio astronomers first started generating images of sources, they wound up with essentially images that were just shades of gray - ranging from pure black to pure white. Each shade represented the intensity of the radio emission from a particular part of the object. Radio astronomers took their shades-of-gray images and converted them to color ones by assigning red to the most intense radio emission and blue to the least intense emission recorded on the image. Intermediate colors (orange, yellow, and green) were assigned to the intermediate levels of radio intensity. Black was assigned to places in the image in which there appeared to be no radio emission.