I have a Cloud Function that should only be invoked by a GKE cluster I'm also hosting. I'd also like to use Firebase Hosting to make a nice url. If I set up the Cloud Function Invoker role on that function to only allow the service account set up on that GKE cluster, will Firebase Hosting proxy that service account and thus still limit access to the Function to only the Invoker role? Or would I need to use something like Cloud Endpoints to achieve that?
If it's not supported with Firebase Hosting, can I still use the Firebase CLI to at least deploy the function and maintain the Invoker role set up? That is, will Firebase reset the Invoker role to allow All Users each time I deploy the Function?
I could test all this to determine the behavior, but I thought I'd ask the question first in case there's a better approach.