No. On the first drag, the add-on checks how each Environment Texture is wired and only adds what is missing. If nothing is plugged into the texture, it adds a Texture Coordinate and a Mapping node. If another node feeds the vector, it inserts a Mapping node in between. An existing Mapping node is reused as is, even behind reroutes. New nodes are standard Blender nodes, placed next to the texture.

Yes. Every Environment Texture connected to the World Output turns by the same angle in the same drag. This works through Mix Shaders, Light Path setups and reroutes.