Yes, it translates on every serve. That allows to use the translation tool integrated into the website. In my case, all translations are cached in RAM, so this is reasonably fast. It takes up only a small fraction of the time needed to serve a completed document. There are also authentication checks, flood checks, bot checks, database access, logging, compression for network transport and a multitude of other things that have to happen when you serve highly dynamic content on a public server.

So, at least in my case, on-the-fly translations really don't really make much of a difference...

Of course, nobody is stopping you from putting your documents through TT and caching the results.