"Adventure Mode" began as a joke where players were told they had to "Unlock" it by finding the golden brick. The joke part was that the rules on how to unlock it were just made up as users posted in an attempt to somehow solidify the claim that it existed. You can't unlock it because it's not there and the Golden Brick/temple/anything these shmucks say, doesn't exist. Don't waste your time and don't listen to them.
The short answer is no, Adventure Mode does NOT exist.