Ah, you are correct vonGenf, the original Janissaries were conscripted slaves. Though kidnapped isn't a term I'd use personally, especially seeing as how well off they were in comparison.
I imagine there were some families that would let them go voluntarily in hopes of a better life, yes. However it is probable that most of these kids never saw their parents again. 6 years old is very young, most of them must have completely forgotten their origin by the time they reached adult age.
Edit: This sources implies, as you say, that most would volunteer to become Janissaries.
http://history.howstuffworks.com/history-vs-myth/slaves-ottoman-empire.htm
