I did my join, then got to thinking about materials. Looks like if the stairs have no material, and they get joined to a pyramid which does, that the stairs get assigned the material. It also looks like if the stairs have a different material, and they get joined to the pyramid, the pyramid then ends up with two slots, and the stairs keep their material. Which is pretty cool! 
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Yes all materials are preserved, just join into one set of slots. All works very well Blender.
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