It is totally possible, and it isn’t hugely complicated. But it is beyond the scope of what I can offer to do for free.
You can easily figure out how web fonts are embedded on your main website and copy the same functionality over to osTicket Awesome. It might look something like this:
@font-face{font-family: 'Your Font'; src: url('../../your-main-website/assets/font/yourfont-webfont.eot');
If you already have the fonts stored on your server you could simply call them using that path. Then it would just be a matter of overriding the fonts you want to change using CSS. Here is a quick example of what it would look like.
body.client-side,
body.client-side #landing_page h1,
body.client-side #landing_page h2,
body.client-side #landing_page h3 {
font-family: 'Your Font', sans-serif !important;
}
If all of your mods are CSS-based (like the ones above) you can drop them all in Admin Panel > Theme > Custom CSS. That way the mods will persist after an update.
But keep in mind that if you end up having to modify any files you will want to keep a note of what you did, because you’ll need to manually re-apply the same tweak(s) after any update.
If all of this is beyond your skillset you can always hire someone to implement this for you using a service such as freelancer.com.
Good luck!