You wont be able to pull lightning components if you are in site.com studio mode.
You will use site.com studio to build your original templates or the pages and then switch over to the community builder to pull your lightning components to add to the site.com pages or community builder .
To assist you with same below is the screenshot to help you
The one is blue will help you to create site.com templates while one in Red will help you to drag lightning components to your site.com pages
To answer you in short it is definitely possible to use lightning components inside the site.com via community builder .