@lindagaf Yes, and your example is a good one. If a student has a thirst for knowledge in a subject not offered by the school, go ahead and self study. If the student plans to go to a state school that gives AP credits like candy, go ahead and self study. However, that was not the question the OP asked; s/he’s clearly looking for validation that self studying a bunch of AP’s will improve the application, and I firmly believe that it will not. Few schools are looking for pure academic drones with nothing better to do with their time.
Edited to add: This topic has also come up on the fallacies thread:
http://talk.collegeconfidential.com/discussion/comment/19868209/#Comment_19868209