Hi Martin,

Yes, this is is possible. You have to create your custom controller which will be handle file uploading and creating media object.

Example :

if (ApplicationContext.Current != null)
    {
        var ms = ApplicationContext.Current.Services.MediaService;
        //Use the MediaService to create a new Media object (-1 is Id of root Media object, "Folder" is the MediaType)
        var mediaMap = ms.CreateMedia("Test", -1, "Folder");
        //Use the MediaService to Save the new Media object
        ms.Save(mediaMap);
    }

http://our.umbraco.org/documentation/Reference/Management-v6/Services/MediaService

Also you can use this tool for media uploading. http://our.umbraco.org/projects/website-utilities/desktop-media-uploader

Thanks, Alexander