In the ED universe, the answer to the ancient philosophical question "if a tree falls in the forest and there's no-one there to hear it, does it make a sound?", is, "No. If no-one is there to hear it, then neither the tree, nor the forest, nor the entire planet and star system, actually exist.".
As noted in the video, the Stellar forge works like this:
First, the stars are "condensed" out of the cloud of available galactic matter. Then, the game calculates probability-clouds of potential planets formed around those stars. It then does a quick flash-forward of the star system's entire prehistory, including procedurally-generated catastrophic interstellar events that might disrupt those nice neat planetary orbits.
It then creates the entire star system, with planets, moons etc, at "time = 0", probably January 1st 3300. It then fast-forwards the planets in their orbits to the correct current time, calculates what the skybox should look like, and creates a game instance to place your ship into it.
It does all this during the hyperspace "loading screen".
Perhaps the most important, significant thing to note about procedurally generating a universe this way: once you leave the system and the instance is closed (and assuming no other players are there in-system), nothing about the star system gets "saved onto a database somewhere", except perhaps some exploration and BGS data. The entire star system - trees, people, planets, everything - simply gets deleted, forgotten about by the game until someone else visits it (or requests to load the system map), when it will all be re-created all over again by the Stellar Forge.