Yes. 100%. As useless as words are in that respect though, they're one of our best tools and I'd personally put music above words there. To convey feelings or emotions exactly is ultimately futile, but some people have the gift of crafting those words or music or images together that can unlock your own (perhaps similar?) state.
One can easily put into words the reasoning behind the way they feel, whatever the emotion. That, is easy. To describe the feeling itself, though? I think you're right about music and how it helps us relate our place in the realm we all share to another. We may not be able to reproduce what we feel in others - not yet, perhaps - because we all experience the world in different ways. What we can do is to channel the emotions into a work of art, whatever form it takes. There are stories as moving as the best pieces of music. Words aren't useless. They just aren't what we'd hope they'd be, given how powerful they may be at times.