MOE did something similar with our VEX in a Day Competition that we put on for the local Ulster Project. There were nine Vex teams consisting of Northern Ireland Catholic and Protestant students, their host students in the US, and a MOE student serving as a Vex mentor. They arrived in the morning and had until 1:00 to build a robot when the games began. And they had to learn how to build a robot as well. The robots were just simple square bots used to just push around balls, but the competition was more spirited than you would think. Below is a link to the post on it, and a link our site that describes how to put a similar competition. Also on the link is the video of the day's competition. (I love the Irish accents).
http://www.chiefdelphi.com/forums/showpost.php?p=527767
http://www.moe365.org/ulster2006.php