Can I learn enough through self-study to pass most security certs?

You bet! It will take time, study and a conscious effort to obtain hands-on experience to prepare for most security certifications, but the same stats that hold for other IT certifications also hold for security certs -- namely, that slightly over half of all exam candidates prepare exclusively through self-study. Get some good books, some practice exams and participate actively in relevant online communities, and you too can fit yourself into this half of the candidate population.