"Ein Mann sieht Rot."
A good question.
Most newspaper and the duden seem to write "sieht rot", in such a context. I have found a few references where it is written as "sieht Rot". This seems mostly when the article is about a soccer player getting a red card, in which case it makes sense that "Rot" is used as a noun.
In summary: without context, it is probably not a noun, but can be.
As mentioned above this usually means the man is very angry.
In German there is an adjective red and a noun red.
"Rot" meaning the color red. "rot" meaning the red car.
And in this case it is written with a capital R and therefore a noun, meaning the man sees some thing described as red.