Will universities consider that my school doesn't offer AP courses, and give extra credit that I self-studied for exams?

I have friends at private schools who do the same thing, so especially with kids looking at elite schools or kids who go to private schools, self-studying for AP exams is common. This will reflect positively on you - especially if your school’s classes are “AP-like” in difficulty, so hopefully studying for the APs shouldn’t be too hard. In terms of coursework, you’re only compared to the other kids at your high school, so Admissions Officers will see that because your school doesn’t teach any AP courses, you’re not penalized for not taking any (officially).

By submitting your counselor recommendation letter, it gives insight into your school, so if college admissions officers read this, they'll be aware that your school did not offer AP courses. If they also see on your application that you self-studied for AP exams and did particularly well on them, then that will work in your favor. Hope this helps and comment if you need any clarification.