Yes, they do. But no more so than the world looks up to J'onn, or half the galaxy looks up to Diana, or Gotham looks up to Bruce. Clark only represents hope from the same metatextual perspective that says Kyle isn't The Real Green Lantern or Babs is More Iconic as Batgirl; that's meaningless to Diana, who works within the context of the actual canon, where things like "The Real" and "More Iconic" don't even exist, and Clark doesn't stand for hope any more than any other really famous, well-beloved superhero, like, say, her or J'onn or Flash, and all of them inspire a lot less hope than a Green Lantern, who's a symbol of hope to quintillions of lives around millions of suns at minimum.
Trinity's been trying to sell us on a meta line; the universe-warping stuff is sheer metatext and deals specifically with the characters as icons, not as characters. Busiek was very careful to establish that, were it not for the Dark Trinity messing with the universe, none of this would be remotely possible, and the loss of Superman would result in a seamless replacement of his position by the universe. If there were no Clark, Tomorrow Woman would take his place. If there were no Tomorrow Woman, someone else would. Clark may symbolize hope to Diana, but that's her thing. It's not sewn into her universe. Quite the opposite.