If you are including the SVG via img-Tag then Hugo can’t help you with this task.
If you are including the SVG inline in the HTML of a layout that is processed by Hugo, then you can define something along the lines of .surroundingclass svg tagname for any tagname inside of the SVG to style it.
SVG files themselfes don’t “fetch” anything from SCSS, as these are unprocessed stylesheets and not available to the SVG file itself, mostly outside of the webroot directory. One is used while creating the website and the other later on, when serving the website.
If you want to CREATE SVG files with hugo, that’s possible via custom output types and in THAT case they might be able to fetch something from the assets directory.