Yes you can do this. Each WordPress link in the navigation has it’s own ID…so all you would need to do is add that menu ID in your css, then add a background image so it only shows up on that particular navigation item.
Thank you. The hard part was finding the ID for the custom home link. I found this tutorial which explained how to not only find the ID of the custom home link on the navigation bar, but also what code to use in the style.css