I'll be getting my MBA in 8 months. Does that count?
The way I look at it, a thank you from you to them communicates, "Thank you for giving me the opportunity to bid and thank you for thinking that I am capable of taking on this job." Of course, one doesn't want to put it exactly that way, but that's ultimately it. They evaluated you as a potential contractor and determined, at least on the preliminary level, that you were capable of and suitable for the job.
My impression of how the hiring company will view it is that you're the kind of person who keeps on top of what they are expected to do and follows up well. Two very positive things for them to think of you. It may also reassert you (and their project) in someone's mind, possibly accelerating their decision-making process.
My thought is: send the thank you.