This website is to check out Google Sites and report my findings. 

Question: How easily can I connect a domain name. What about subdomains?

Answer: 

I was able to connect a subdomain to this google site. There appears to be no additional cost, and my domain is at a third-party registrar(the domain name was not bought through Google). My registrar, PorkBun.com, had instructions for the DNS settings specific to Google Sites.