This is like asking if Fritz Lang's Metropolis
(1927) looked dated to audiences in 1966.
I was aware of Star Trek's production limitations when I was 15 in 1966, especially with its obviously fake "exterior" sets built on a soundstage. The Enterprise model looked strange, because it didn't look like previous film spaceships, but that was the intent.
Does it still look futuristic to me? I accept it for what it is-- a product of its (and my) time on this tiny speck of dust in the universe.