Good question! The unsatisfying answer is "it depends". The more satisfying answer is "yes, if you wait long enough".
Metonymy is generally a poetic device. Sometimes it's made up in a particular instance by the poet/writer/speaker, and sometimes it's fairly entrenched (like the "force of arms" you mention).
However, over time, metonymic meanings can become well enough established that they overtake the original, literal meaning of the word. For example, the Latin word cancer originally meant "cage". Through metaphor, it came to mean the claws of a crab, which close around something. And through metonymy, it came to mean the crab itself. By the Classical period, that was the primary meaning of the word.
This is a fairly standard type of semantic shift, which can be found in all sorts of well-established words if you look back far enough. Even something as straightforward as "person", for instance, has a long history leading back to a word for "mask", which changed to "character" by metonymy, and then "personality", and so on.
So while "arms" still means "weapons" more than it means "war", in a few more centuries it's entirely possible that the "war" meaning will have displaced "weapons" and become the primary one.