The download currently does not work – it gives an internet connection error. This is to be expected. I would fully expect that the download will work after 12:00am EST Thursday.
We have the Wrath downloader up at our sister site Big Download for the PC and MAC (which runs on AOL networks so it's not going to go offline), or you can get it from Blizzard's site (which we all know goes offline when more than 10 people decide to view it at once). If this is your only way to get Wrath tonight, expect to have to wait a bit for the Blizzard downloader to work – but you'll at least get it.
Update: It should be noted that since this story went live, Blizzard has said this download is currently unsupported. Of course, this could change quickly - and we fully expect it to change around midnight tonight. Be assured: the download is from Blizzard and by Blizzard. Not some third party site.
Thanks to AngryJoe for the Mac information!