I wouldn't mind at all; I got a lot of these when I was looking for work. It was nice to know that they got it, so I didn't have to resend it.
What bugged me, if I hadn't heard anything after an actual interview, was that sometimes no one had any answer for me when I followed up, or never bothered to let me know that the position had been filled. Even a postcard would have been nice. I usually checked back twice and then gave up if I didn't hear anything. That's the only time I felt brushed off.