In worker mode the runtime runs in a WebWorker. WebWorkers are considered a separate "thread" that runs along side the main "thread". Threads cannot directly access each other, which means they can run on independent CPU cores and hence not interfere with each other. The only way they can communicate is to send messages using the MessageChannel API.
Cordova code has to run on the main thread. As you cannot read/write to the variables of other threads this means it cannot be accessed from a WebWorker. For Construct plugins that need to run on the main thread they register an additional script that the runtime knows to start on the main thread, which can send/receive messages from the main part of the plugin.
I don't believe we have a mechanism for registering a user script to run on the main thread yet. So if you want to interface directly with Cordova plugins you will not be able to use worker mode.
Incidentally "window" is not the global object in worker mode, and in fact doesn't exist...
If you want to listen to changes in sign in state you need to use the "setCallback" method that Eren mentions.