Valid SSL certificate for domain/subdomain pointed at a private IP address

There is no difference between private (RFC1918) and public IP addresses except that the former are not routable on the Internet and the latter are.

Your DNS zones can point to both these private and public IP addresses as to the DNS — and to routers and other devices — there is no difference between private and public IP addresses. Your SSL/TLS certificates aren't concerned with IP addresses at all and only care about DNS names. Your certificate is valid if it is signed and you use it on the correct website.

Thus to answer your question, your wildcard certificate will work and be valid as it is a wild card certificate for your domain. The IP address pointed to by the A record is of no significance.