Yes, it is implied, but I dislike implications within a definition, even when they are correct. And I believe a general reader may share the sentiment, or even get confused.

Decades ago, before computers, it was important to make simple equations even simpler. To that aim, static equilibrium was used in some accelerating system problems, of course with the inertial forces included (the approach was credited to dAlembert). A simple example would be to determine maximum acceleration of a motorbike for a given friction coefficient (no limitation on engine power). When solved in the accelerating frame in which the center of mass was at rest, one could use torques about any point (as both static equilibrium conditions apply) and achieve minor simplifications in calculation. As I recall, one would casually refer to that accelerating frame as "the motorbike CM frame". Why not, the meaning was perfectly clear, and what authority might there be to forbid such usage?

That being said, I am aware of the fact that relativistic particle collisions are best described in inertial COM frames. Some authors call them "COM systems", as e.g. in the Sears and Zeemansky College Physics. (They even claim that "COM system" is a relativistic generalization of "CM system" - people will use various conventions.)