While there is no limit to the number of people that can download the network test client, there is a time limit for when it will be available. Specifically, the client is only available to download until 11:59 PDT, May 8 (2:59 AM EDT, May 9). If you don't grab it by then, then you won't be able to participate in the network test a few days later.

There's another side to this that's worth noting for anyone that prefers to stand by their "Prepare to Die Edition:" on May 9, that version will be removed from the Steam store altogether. If you own the game, then you're fine and won't be affected by this change at all. If you're looking to pick it up, then after May 9, you'll only be able to get Dark Souls: Remastered. The main reason why you'd want to pick up the current/old version of the game is if you're interested in checking out the various mods that have been created for it, which includes some interesting randomizer mods that move around enemy and item placement throughout the world.

No specific reason was given for the delay. The Bandai Namco account stated that it was because of "various reasons," while the official Dark Souls Twitter account pointed towards "the nature of causality," which, let's be honest here, is a pretty Dark Souls NPC thing to say. That account then went on to say "Rest assured, this time will ultimately be used to improve your journey to Lordran," and also confirmed that there will still be a beta/network test of the game on the Switch, though the dates for that are still unknown.

Based on the announcement from Bandai Namco, it sounds like the online player count will be increased for Dark Souls: Remastered from three (plus one invader) to six (with who knows how many invaders). This means you and up to five of your friends can team up to take on the Capra Demon, Bell Gargoyles, and Ornstein and Smough. In addition to the base game, the remastered version will also include the "Artorias of the Abyss" DLC.