Keep in mind, adding local entries to your external DNS will expose internal details of your network, such as hostnames and IPs. Same goes for Let's Encrypt, due to Certificate Transparency logging.
While you'll get the hostnames leaked - you could register them as fake addresses (say an A record for 192.168.0.1 for every address), and have a local DNS server overriding with the real addresses. Whether this is worthwhile or not is debatable. Is the fact your internal server 'gubbins.mydomain.com' exists, or even that it exists on 10.0.41.43 really much use? The other option for internal certificates is to get a…
Pretty much this. What does it matter if you know certain hostnames or internal IPs on my network? It's all firewalled anyway, and if it wasn't it would be trivial to find them out on your own...