Hi CCChris, the CDN would be caching your origin files from the origin server; and from time to time the cache is repopulated. It is important that the images reside in your origin server so that the CDN can cache it at any time. Once your site is integrated with MaxCDN through a CDN Plugin (like W3TC or WP-Supercache or CDNLinker Lite), the caching is automatic and you don't need to upload images in the CDN. It is important to note that the CDN's purpose is to distribute your content and make your site faster, but should not primarily serve as your origin server.
In MaxCDN, we do have PUSH ZONE where the files reside in the CDN servers, but it is not advisable for small files. But if your traffic and files are really huge, we can also help you explore that option, but push zones are normally used for large downloadable files. Email us at support@maxcdn.com with the details and we can help you more personally and faster.