setup firestore without auth, but using a (key,signature) data

Question

i want to setup a firestore-redux integration into my web app but instead of using the auth to email authenticate and define 'users' collection, i'd want to know if it is possible for a user to use his private key to sign a message and store the hash as the "auth.uid" for firebase? example: instead of using auth config like this:

// react-redux-firebase config
const rrfConfig = {
  userProfile: 'users'
  UseFirestoreForProfile: true // Firestore for Profile instead of Realtime DB
}

and instead of setting security rules like this:

// security rules    
service cloud.firestore {
      match /databases/{database}/documents {
        // Allow only authenticated content owners access
        match /some_collection/{userId}/{documents=**} {
          allow read, write: if request.auth != null && request.auth.uid == userId
        }
      }
    }

can we have a custom config where the document key is the user's public key which is verified in the security rules (for read and write) using the signature hash of user's private key?

// react-redux-firebase config
    const rrfConfig = {
      userProfile: <<some public key or ethereum address of user>>
      UseFirestoreForProfile: true // Firestore for Profile instead of Realtime DB
    }

// security rules    
    service cloud.firestore {
          match /databases/{database}/documents {
            // Allow only authenticated content owners access
            match /some_collection/{userPubKey}/{documents=**} {
              allow read, write: if request.data.signHash!= null && request.data.signHash == resource.data.signHash
            }
          }
        }

This will be relevant when using ethereum (blockchain) account based authentication for firebase storage, instead of the usual email based.