Can I override or create a new Dropfiles theme?

You can customize and add theme to Dropfiles, but we don't use the standard MVC Overrides but the Joomla default plugin system.

Dropfiles themes are in fact plugins and they are located in the folder /plugins/dropfilesthemes

You'll have to copy one plugin, change the name of the plugin to create your new plugin (pluginname.xml and the class name of the plugin). Then install it through Joomla standard installer, it should be shown in the list of themes. You can then do all changes you want in this theme, it will not be affected by updates.