Do graduate school admissions appreciate individual "free time" study?
I have limited knowledge about this and I speak from experience as a graduate student who has gone through a similar situation (from the outside) as well as being the student representative on our graduate admissions committee (on the inside). Obviously, a professor or academic with much more experience than I have can attest to this in better ways.

In general, formal education is given preference. Grades in relevant courses are given more importance than others. Note that there is a lot of competition for slots in a PhD program. Self study is a very fuzzy area and there is little scope for the graduate admissions committee to evaluate it. There exists of course, two mutually non-exclusive ways exceptions to this general norm:


A respected recommender in the area attests to the fact that you did engage in significant amounts of self study and that has contributed to your overall knowledge.
You do self study. Then you do research based on it. Then you publish in a non trivial journal or conference. That automatically attests to your knowledge in certain ways.


Otherwise, ask yourself this, why would graduate admissions committees believe you, especially when there is usually bound to be a few more well qualified applicants with good scores in relevant courses?