Statistically I don't see it making sense. Assuming the traffic clicks as it does with normal keyword you'll get less than 10% if you're not top 5 (I can't remember the exact numbers) but unless you were giving away ipads or the other sites have some shitty/mediocre content, I'd still think it's a long shot. Are you doing anything to encourage them to link?
You're talking about traffic and I'm talking about webmasters linking.
Obviously it's going to get a lot less traffic for the average visitor, but we're not talking about average visitors. We're talking about webmasters.
Webmasters don't fall under the same category as visitors. When you go search for a topic do you automatically click the first ranked site in Google? I know I don't... it's usually pretty easy for an experienced user to spot quality sites. Thinking as a webmaster, if I'm writing an article or blogpost and I want to reference a topic, I don't just google the keyword, and take the #1 site. As a webmaster I'd want to link to a quality site, if I see an .edu site with great information, obviously I'm going to link to that.
That being said, I think you were confused a bit by what I initially said. I'm not saying I'm going to get more links than #1. What I was saying that once I'm in the top 10 I will be getting more traffic, and more chances of getting organic links. And being a .edu site (with great content and research), I'll have higher chances of getting links at #10, then a commericial, or even regular site. As I move up the top 10, hopefully I can more and more organic links, as I continue to build links myself.
In short, if I get into top 10, it will have more exposure, increasing chances of organic links being a well put together .edu website.