What is a private registration?
You trust a registrar to register your domain name under their name. So when a whois query comes in, it shows the registrar's private registration info. So technically you do not own a private domain.
Google doesn't use regular whois to query domains. They have a back-end system that queries domain data in bulk.
The back-end systems can be standard or proprietary.
When they do a standard query, then Google cannot see your data. They would see the same we do.
But for proprietary B2B deals, maybe they can. We don't know. As some mentioned there's GDPR and similar laws, but I'm not familiar with how domain data sharing actually happens for large registrars.
For example, financial institutions have back-channels to customer data. Some banks know you before you open an account there.