Pros and Cons of Buying Diablo 3 hard copy vs digital copy

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.

If you purchase it from Blizzard I believe you can pre-download the game client. For example I have the WoW Annual Pass and have already downloaded the game client. You will then only need to download the release patch (assuming there is one). However it is likely that this is only going to be relatively small. Overall I would suggest getting a digital copy unless you really want the artifacts of the hard copy (DVD, etc).