The account looks real enough - the naming scheme follows a lot of celebrity tweeters' styles (theREALdvorak, theREALbritney, etc). The website linked to the account even looked official enough, with prominent logos and links to all of Al Gore's various ventures and projects.
Something about it all set off my hoax-o-meter, though, so I decided to do a bit of late night investigation.
The first thing that caught my eye is that the list of followers reads like a who's who of the A-List. It starts with the Twitter staff like @ev and @biz, and works it's way down to folks like @laughingsquid, @xenijardin and @scobleizer. Combine that with the fact that the follower/followed ratio is something like 102/1600, it's obvious that there's an adding bot involved here (or an intern with a very sore clicking finger).
The first two tweets were a little suspect, too. The first one says: "invented a new blog @ www.aninconvenientblog.org", and the second tweet says: "world's first blog post...http://tinyurl.com/65ezrt." I've never met Al Gore, but I can't imagine him playing on his widely known faux pas in such a cavalier manner.
Both links bring you to a blog post where Al Gore is supposedly congratulating President-Elect Obama on his big win, and alluding to Al Gore's role in the new administration:
As many of you know, I am good friends with Barack. I called him earlier today to congratulate him on his victory over Senator John McCain.
I look forward to serving in the Obama administration and while I cannot yet reveal what my exact role will be, I can assure you that President-Elect Obama and I are eager to get started building a new world. One that is green and sustainable.
I took a look at the DNS records, but they provided no real clues (only more questions). The DNS information was protected by a standard anonymizing service out of Canada.
I did an informal poll of a few folks who were chatting with me via IM at time the Twitter notification came in. All of them had just received an identical invite, and all of them responded pretty uniformly, along the lines that it appeared to be an expertly done forgery.