This sounds like an original composition, so yes you certainly could write about that. Make sure that you have a strong thesis statement that is interesting at the same time. Something like,
The grey envelope had the outlines of Harvard University’s crest imbedded in the paper. I was excited that my life had finally begun. As I carefully cut open the envelope, images of ivy and expensive polo shirts floated through my mind. All seemed right in my world until I read, "we regret to inform you that...."
My point is that it is good to begin with something creative. After that you can state your thesis about how it made you stronger.... Come up with two or three good reasons why your rejection might not have been a bad thing. Perhaps you were not ready for it or perhaps it taught you to be more humble and work harder. Make sure you give concrete examples no matter what main points you choose. I think it is a good idea as long as you can convey that you can contribute to whatever school you end up in. Good Luck!