You can pre-download Diablo 3 once you've purchased it online. As @dlanod mentioned, you can generally pre-download Blizzard games.
However, to more directly address the question you have proposed you need to remember/be-aware that Blizzards downloader is a Peer to Peer downloading scheme. They use small feeders to populate different sections of the game to different people and then all of those people are offered up as hosts to everyone else to get those parts.
So the situation is not really a few hundred thousand people all hitting one or two servers for the game, but a few hundred thous and people all getting a small piece pretty quickly from the server like normal web browsing or MMO traffic or whatever, and then sharing that with everyone else as long as they are downloading.
There should not really be any release day concerns with access the server to download the client to your system.
The update you just downloaded was not to the game itself, but rather to the Diablo III Launcher. Because the Launcher update has no actual impact on gameplay, it can get pushed out at any time, and it does not matter whether your friends have updated it.
Other gameplay updates will come in the form of either Patches or Hotfixes.
Hotfixes will be announced on the Diablo Website or forums (sometime a few hours or days after the fact), and are applied server side. These do not require you to download anything, and your gameplay experience will reflect the changes immediately. Occasionally, these hotfixes require Blizzard to restart the games servers, either momentarily, or for an extended period. Either way, everyone is up to date because all of the changes are server side.
Patches will generally only occur in conjunction with announced server restarts or downtime. You will not be able to connect to the game with an out of date client, and before the patch goes live, you will be disconnected, as the servers go offline for Blizzard to apply their side of the patch. If you never close the game, you won't get the updates, but, since you'll have been disconnected, you also won't be able to log back in - after the update goes live, your attempts to connect to the server will be rejected until you update to the newest client software.
Best Answer
Yes you can, the game can be installed to any location and then played from there as long as the entire game is self contained in it's own folder. The game performance may suffer a little because it is being accessed via a data cable which is generally slower than an internal hard drive.
This also helps in terms of moving the game around from computer to computer/hard drive to hard drive.