[Vuejs]-Vue call component inside background-image

You’ll need to access the icon’s SVG directly, not through the component.
Assuming that you use webpack and npm, and your icon lib contains SVG data (i.e. it’s not wrapping the images in JS files, like e.g. vue-awesome does): you can just write the relative path to the SVG file into the style, in which case you don’t have to bind it (style instead of :style).