Yes. That is what most caching feature does. Take Ruby on Rails as example, if you have a static page, you can just cache it as just raw HTML file(after the first rendering).
That's what caching does, but it's not exactly the same use case. Jekyll just generates a folder full of static HTML files that I shoot out to a dumb server that doesn't run Ruby. I'd like continue to do this, and just run a shiny interface locally.
To do the same thing with the cache in a Rails app, I'd probably have to make a script to visit every page to get it to render to the cache, then copy the cache out. At that point, it'd probably be easier to ignore Rails' built-in caching and just to make a rake task that renders everything.