I don’t think I understand what you mean by “make available on the back end”, nor what you’re intended usage is: “used in custom CSS code”. If you could elaborate, I may be able to provide a better response.
But here’s what I’d say based on what it seems like you may be asking:
(1) The only way this plugin currently supports loading Font Awesome is via CDN. Thus, if you are using the Webfont/CSS technology, there’s never a time (with this plugin) where the webfont and CSS assets are loaded and available on the backend (WordPress server). Instead, the back end code adds the appropriate HTML to your page templates to cause the configured version of Font Awesome to load from the appropriate CDN URL.
(2) If what you mean by “custom CSS code” is writing CSS pseudo-elements, then you can still do that, even with how the plugin works. Here is some guidance on using CSS pseudo-elements for Font Awesome.
(3) If you have a use case that requires having the CSS and/or Webfont assets available server-side, then this plugin is not what you need. You’d need to instead “self-host” the assets: store the assets on your web server, and enqueue the CSS like any other CSS being served from WordPress server. I don’t think this would buy you any increased functionality in terms of using it in custom CSS code, though. And you’d lose the loading optimization of loading assets from the CDN, so it may also be slower.
