CyberGene GreXXL I'm pretty sure it's the opposite. In runtime mode, nothing is stored. The XML sitemap is generated on the fly when queried by search engines.
Generating on each content change would be prone to breaking because if any issue happens (like for example the SMTP server being down and email failing to send, or any kind of bug in another extension) it could result in an outdated/broken sitemap. And if the full sitemap was generated every time a discussion is created or edited, it would cause even longer response times for users on a site that doesn't use a queue, so it would be really counter-productive to use this option for hostings that are already quite limited. Instead only the search engines have to wait for the sitemap to be generated, which should have no impact for regular users.
In any case if you can use the scheduler to generate the sitemap you'll have the best solution overall, with no load time impact for both customers and search engines.