Arnold Schoenberg: Classic or Dud?

^^^ gets it.

No, you should not need heavy intellectual investment to appreciate his work imo - he himself had very little formal training and was mostly self-taught. He was an Expressionist and a Romantic. (Analysis can certainly help but it is not and should not be the only way his work can be approached.)

To Kandinsky, he wrote (from Ross, The Rest Is Noise):

Art belongs to the unconscious! One must express oneself! Express oneself directly! Not one’s taste, or one’s upbringing, or one’s intelligence, knowledge or skill. 

To Busoni (from Auner, Music of the 20th and 21st Centuries):

It is impossible for a person to have only one sensation at a time. One has thousands simultaneously. And these thousands can no more readily be added together than an apple and a pear. They go their own ways. And this variegation, this multifariousness, this illogicality which our senses demonstrate, the illogicality presented by their interactions, set forth by some mounting rush of blood, by some reactions of the senses or
the nerves, this I should like to have in my music.

Don't get me wrong, he (despite his lack of formal training) became a famous theorist and teacher (and then professor) as well and there is a lot going on formally - but he would have definitely been happy with people appreciating his music in a visceral, immediate way.