Is Shi Zhushan in Praying for a Dream asleep?

No, it's a spiritual sustenance.

The custom of praying for dreams in Shizhushan was formed in the Song Dynasty. It takes the belief in the Nine Immortals as the spiritual link, along with the wisdom of life and seasonal customs, and takes the folk psychological medical knowledge as the connotation, forming a unique and rich dream culture in Shizhu Mountain. Since the Ming Dynasty, not only a large number of Fuzhou people, but also good men and women from all over the world have come to Shizhu Mountain to burn incense, beg for visas and make wishes. People call Shizhu Mountain "Nine Immortals' Dream Prayer", "Dianthus Wonderland" and "Chinese Dream". Shizhu Mountain is known as "China's dreamland", and "dream culture" is a major feature of Shizhu Mountain's religious culture, so it is known as "China's dreamland".