If the security rule for read/write access is set to require auth will firebase-admin be able to read/write without authentication?
The Firebase Admin SDKs access your database using a service account. Service accounts ignore the Cloud Firestore Security Rules, similar to how you can edit documents in the Firebase Console directly yourself.
Taken from the Cloud Firestore Security Rules: Getting Started documentation:
Note: The server client libraries bypass all Cloud Firestore Security Rules and instead authenticate through Google Application Default Credentials.