Not necessarily. Art can communicate horror, humor, sadness, tragedy, etc. Just so long as it communicates.
That is the one of the great failings of Modernism: it is poor to non-communicative. "What does it mean to you?" is a cop out by artists who either don't know what they are trying to get across, or are inarticulate in their medium. The inarticulate then either mumble and scrawl, like Pollack, or scream simplistic statements, such as "Piss Christ".
But there are exceptions, and sometimes they occur in the oddest places. I saw a guy in Japan do simply astonishing things with only his hands and colored sand. Then before he left he'd wipe them slick. I asked him why he didn't preserve his stuff (my Japanese was worse than his English, which wasn't very good) and if I understand what he was trying to say correctly it was on the order of "you can't, and if you could you'd miss the point." Somebody told me he was a rice farmer.