Hi Dario, ADE (Architect Desktop Engine) is not designed to work with Cordova applications. It can only be used to run Architect Worlds within an desktop browser. You can however use ADE to debug/inspect your Architect World which is loaded/used within a Cordova application. Just make sure that you load the .html page that is your Architect World and not the Cordova application.
Most times I find it more helpful to use Chrome or Safari JS debugging tools in order to inspect/debug my Architect Worlds.