I teach AP World, but there are some questions that I wasn't exposed to in college or the material I teach with, so this question came up today at my morning tutoring.
I've never read anything suggesting that they were. The primary method of recruiting jannisaries during its period as a slave-based institution was through the devshirme which recruited from a quota of Christian boys, mostly from the Balkans.
As the devshirme declined, it was replaced by a system of free-born recruitment of local muslims in garrison or hereditary recruitment from the askari (military) class.