pair system?

[bdalameda]

It doesn't shut off the fuel flow, it shuts off the air flow, thus richening the mixture so that it will burn in the cylinder instead of the exhaust.

You are right. It shuts airflow to the pilot system, stops the atomization of fuel and the sudden lean condition when the throttle is cut that can cause backfires and popping. I thought it stopped all flow through the pilot system but it does not.
I can say without a doubt - if you are getting a lot of popping or backfiring during deceleration these should be looked at.