It's unfortunately going to really depend on how they go about it. The official Synology DSM Let's Encrypt documentation has historically been... questionable. I wrote a clarification/critique a while back in an attempt to provide a starting point for Synology DSM users. I'm not sure if it's correlated or not, but after that writing an update to the official documentation seems to have addressed/dodged almost every concern that I mentioned.
You have aptly identified what is likely the most common case of that rate limit occurring. It isn't specifically limited to Synology DSM, but it is very common due to many/most users trying to acquire/renew a certificate for a subdomain name of a very popular apex domain name.
The main limit is Certificates per Registered Domain (50 per week). A registered domain is, generally speaking, the part of the domain you purchased from your domain name registrar. For instance, in the name
www.example.com, the registered domain isexample.com. Innew.blog.example.co.uk, the registered domain isexample.co.uk. We use the Public Suffix List to calculate the registered domain. Exceeding the Certificates Per Registered Domain limit is reported with the error message too many certificates already issued, possibly with additional details.