No, the NS records are needed in order to tell the Internet (and specifically Let's Encrypt's servers) to query your acme-dns instance for the acme.yourdomain subdomain. You'd still need CNAMEs for any hostnames you'd want to get certs for, but the client/auth script will tell you what those need to be, and they ordinarily only need to be created once.
Edit: I had some trouble wrapping my head around acme-dns before I started using it; this topic covers some of the basics: