It would make sense for them to not include the Systems you can't reach yet into the Game already. Since unused Data is just a waste of Money to store on a Server - also it is always good to not give People even the smallest chance of breaking out of Game Mechanics (People always manage to do things Developers thought would be impossible).
I looked up a Video from JC about the Procedural Generation and I believe you are right with the correction that everything is procedural (I probably got it confused with Star Citizen - there they use Artists to make the Procedural Stuff look more natural).
As to a finite or infinite Universe: I know you said technically infinite, but I want to press the matter again: Infinite is not possible.
But to go more into depth, I remember JC saying that they store the base of the Universe in the Procedural Algorith, (Mathematical Form - Compact and basically no Data Cost). But everything the Players do to derive from that Mathematical Description is Stored on the Servers. And that will accumulate to a lot over the Time. If then the Universe is really big and Players begin to make Crazy stuff it will start getting really costly on the Storage side of Things. So my guess would be that they limit the Size of the Universe so that you would generally speak of a finite Universe and not an infinite (even if you speak in non technical terms where you would call finite sizes infinite (like say No Mans Sky where the Player can not customize every Planet to his liking and generate tons of Data and on top of that DU is a MMO where not 1 Person does this to his own HardDrive but Hundreds of Thousands of Players do it to the Server)).
You are right about the Procedural Generation: It seems DU will generate everything Procedurally.
I disagree on there being the whole Universe in Place at the Beginning of the Game since that would not make sense in multiple Cases.
I don't think you can speak of a technically infinite Universe since over time the Players will let the the Universe derive that much from the original Mathematical Description (which is cheap to store) to a Point where it will be really costly to Store that amount of derivation Data and there will be a Size Cap. In comparison to Games that can be technically infinite because they don't have to store Derivation from the Mathematical Description (like NoMansSky).