No, it’s made of stainless steel. A fraction of the price of the equivalent in composites, and lighter than the composites plus heat tiles.
Musk says the machine will use tiles, although originally there were thoughts of using coolant between skins or, perhaps, transpiration. Per Musk's tweet, 24 September, 2019:
Could do it, but we developed low cost reusable tiles that are much lighter than transpiration cooling & quite robust
Also, the rocket will be powered by six engines, not 27; three are optimized for atmospheric use and three for vacuum conditions.