Yep. The Emerald tournament held in Seattle in 2005 was the only official Singles tournament since doubles was created as a format. Off the top of my head I can think of the following official tournaments, all doubles. It's the standard competitive format.
Battle Master (2004 - UK)
JAA (2006 - US)
Nintendo Sponsored GameStop PBR (2007 - US)
Nintendo Connection Tour (Various years, AU)
Video Game Showdown (2008 - US and JP)
Video Game Championships (2009 to 2012 - US, JP, EU, KR, and CA)
WiFi Friendly (2011 - JP)
Damn. Nintendo actually does a lot of tournaments.
I won't be able to participate on the Monday (Sunday American time) due to TAFE, and the next day will also be difficult. How will that affect my ability to participate?
It's just laddering as far as I can tell. So you can play to your own schedule in the days allotted.