Sometimes you never know what you get if you contact a company. My co-worker once wrote to a favorite energy drink company asking for some promotional stickers. She got a box with 50 stickers, some t-shirts, posters, all sorts of cool stuff. Worth a try.
Could send a letter to:
Philip W. Schiller
Sr. VP Worldwide Product Marketing
Apple, Inc.
1 Infinite Loop
Cupertino, CA 95014
Politely explain you're wondering if you might be able to obtain a poster with the Apple logo on it to hang up in your bedroom and mention you've been a longtime fan of Apple products. Make sure you have your name and return mail address in the letter somewhere, too, because they may throw away the envelope.
Might work or might not, but will cost you just 44 cents, an envelope, a sheet of paper, and two minutes of your time. He probably won't personally read the letter, but hopefully an administrative assistant will forward it to someone in the department to fulfill.
P.S. If you write, postal mail makes more of an impact than email. That's why I suggest doing it this way. Also, make sure you spell his name correctly; that's just one 'l', not two, in Philip.