Hi Curtis,
Yes, the environment takes precedence over the application settings. For example, you can run the Clip tool and choose whether or not to build pyramids. In regards to the application settings, ArcMap options will not be triggered until the raster is added to ArcMap. If you have these options set to always build pyramids, and pyramids are absent, pyramids will begin to be built once the raster is added to ArcMap.
1. GP Environment > Pyramid (note, the default is NONE, according to the help)
This only applies to when you are setting Pyramid Environments with scripting.