Can you validate an ACM public certificate using a domain record in a Route 53 private hosted zone?

It's not possible to validate an ACM public certificate using a domain record in a Route 53 private hosted zone.

When you request an ACM public certificate using DNS validation, ACM provides a CNAME record that you must add to your DNS configuration to validate your ownership of the domain. Because anyone can create a private DNS zone and put records on it under any domain name, being able to make a change in a private DNS zone doesn't prove public ownership of the domain.

For more information on DNS validation, see DNS validation in the ACM user guide.