When you type your password into the sign in screen on Windows for a local account it never leaves the machine. That means the NTLM (or Kerberos) protocol is never invoked. Domain accounts are different. They will attempt to verify against a cached login validator (strong one-way hash) first and then will attempt the network by trying Kerberos first and fall back to NTLM if it fails.
However, to complicate the explanation of things Windows bundles authentication protocols into packages and these packages are what provide sign in functionality to a machine whether its a local account or domain account. ALL sign ins flow through the NTLM package first and handed off to e.g. Kerberos for the actual processing.
Local accounts use the NTLM package to authenticate local users. That package is the thing that knows where password hashes and user metadata are stored.
So no protocols are involved during local user sign in.