You will only see about the top 4,xxx,xxx sites with a ranking on Alexa. If their rank is greater than that, they will show as no ranking. Even with a 4 million ranked site, you still may see some traffic from them if the sites linked to them are of good quality.
The ranking is based purely on the number of visits to the site by people who have installed the Alexa toolbar on their computer. If noone that visits your site has the toolbar, then you will have no ranking. If one person (say yourself) has the toolbar and visits your site a dozen times a day, every day, your Alexa ranking will get much better (lower), which really shows nothing about real useful traffic.
So yahoo.com's Alexa rank is 1....not because of the millions of incoming links, but because lots of people with the Alexa toolbar visit that site.
fcisonline.com, on the other hand, is ranked 3,620,128, probably because of a couple of people who have the toolbar and have frequently visited the site......perhaps a couple of the students at the school.
Bottom line.....Alexa is a rough gauge to traffic, but probably not accurate or useful at all until you get under 1,000,000. You need to check the incoming links for quality and quantity, which will give you a better idea of whether to expect traffic.