Technically yes, but since the WM usually comes as part of a desktop environment that also includes utilities and daemons which help with that sort of thing, to many folks "my WM makes a big difference in how easy it is to set up external monitors" is often true.

It drives me crazy that there's not a long running named process in e.g. GNOME the DE that if I run will cause my fn-volume keys on my laptop keyboard to change the volume any WM, the same as when I'm running GNOME? Why isn't that piece separated out? Or at least, where is the code so I can separate it out?

Questions and experiences like that cause many to conflate behavior and experience with WM/DE.