Even if you said you would be willing to move right away, what about when they call you for an interview. Would you be able to drop $800.00 on a flight to get out there ASAP? Also, would you be able to start when they want you to? Most likely not because you will have to find a place to live first and then move (unless you are living in a hotel).
So, even if you put that you would move on your cover letter, there is still an inherit risk for them in trying to hire you. It's best to not even bother with so many applicants already living in the area and available that day.
Also, cover letters are just a way to show you know how to communicate. What you put in them really doesn't mean much to them. As Apple is a big company, they probably put it through a computer screener and only look to see if you included a few keywords that they are looking for. They also do this with your resume. If someone actually reads it, they don't spend any more than 10 seconds reading your resume and cover letter. So, most likely, they didn't even see that information.
I would recommend going on a trip to Chicago, getting a hotel room, and just walking around to find a job. Ask to talk to managers and tell them you are interested in working for them. And don't put all your eggs in one basket. Apple shouldn't be the only place you apply for. They probably got at least 700 applications for the single job that you applied for. How did you make yourself stand out? Other applicants may of had years of retail experience already.
I don't really know what you want to do for Apple. However, you don't have to be so devoted to them. You could get a job at Best Buy, or any other retail store to gain experience and then try the apple store again later. If you want to work for Apple at the corporate office or something (years down the road), any experience will really help. The times of moving up slowly within one company is pretty much gone in today's world. It is expected that the next generation has 10 different jobs by 35 or something like that. And retail is a very hard business to move up in. Every year, retail stores go through a restructuring (usually around this time) and get rid of managers, staff, and bring in new ones.
Basically, what I am saying is that you wanted to work for apple is good and all, but expand your options.