Can a real object "symbolize" another real object such as the natural association of Mount Fuji with the nation of Japan? If so then is "Mount Fuji" a word?

All these musings on whether a "word" which ordinary readers recognize as a "word" is actually a "word" are way over my head, but perhaps we have can agree that "Mt Fuji" is a word if it stands for "Japan" even if we can't agree that it is a word if it stands for Mt Fuji alone.

When "Mt Fuji" stands for "Japan", it is a synecdoche [defined as follows].

3 entries found for synecdoche.
syn·ec·do·che ( P ) Pronunciation Key (s-nkd-k)
n.
A figure of speech in which a part is used for the whole (as hand for sailor), the whole for a part (as the law for police officer), the specific for the general (as cutthroat for assassin), the general for the specific (as thief for pickpocket), or the material for the thing made from it (as steel for sword).

If "Mt Fuji" standing alone [i.e. for itself] isn't a "word", what is it?

And why does this distinction matter if an ordinary reader understands precisely what we mean by this pairing of ... uh, palabras?