AP test scores validate class grades. In most cases they don’t stand in lieu of them. With no grade to validate, and with AP awards simply being participation awards, the score without the class does very little to further your case for admission.
Putting the score in your application probably won’t hurt, but it isn’t going to be what tips the scale in your favor either. On the other hand, participating in ECs that engage with classmates, peers, or the larger community can help your cause. It may be worth spending the time where it can be most effectively used.
There can be non-admission related reasons to self study. For example, you are going to a college that promises to accept self-study scores (not all will) and you are counting on those credits to graduate early, usually for monetary purposes.