At the moment, arcpy and thus the underlying Python functionality in Pro is not a true site-package, the code in arcpy is laid down with the installation of Pro in the Resources directory. As such there are a few special files within Pro environments to temporarily set the OS PATH to include the location of arcpy when python.exe from within a Pro env is run.
If those aren't present in a newly created environment then arcpy won't run successfully. You are correct that creating an additional environment will not affect the one which has the arcpy functionality - you should be able to switch between these without issue - however if you've installed Anaconda alongside Pro you have to be mindful of which conda.exe, python.exe etc you are calling. Since there are essentially two installations of the same program, you will only be able to access the envs associated with the executable that is being run. This is based off the system's PATH variable.
The conda installation in Pro, including its envs, exists within Pro's folders. Any envs outside of that folder structure will not work with arcpy (we are working on improving this, but as of Pro 1.4 it is the case) Anaconda is aggressive in changing the PATH, so if you've installed it after installing Pro your PATH likely points to the non-Pro installation's executables.
A handy command in the cmd prompt is 'where conda' - this will show a list of all the locations conda shows up on your PATH. The topmost one will be executed by calling that command on its own.