Not so, since svg content is in another document. Styles do not apply to documents.
And since svg will be seen as a dumb image when done with CSS, setting the hover style on the path inside svg won't help either.
I would recommend putting svg inline in the document if you want to put some shapes in it.
However, another option for changing the color of an image is to use filters, as they can be applied externally. If your image is simple, that might work.
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