flitt,
Negative. The requirement for bomber flexible guns and turrets to fire is to be off the ground. Even an inch works.
You seem to be kind of thinking of bombs. Bombs must travel through 1,000ft of air in order to arm. That doesn't mean that you need to be 1,000ft AGL though. When you drop a bomb it has the aircraft's momentum level, so bombs dropped from an aircraft traveling at 300mph 100ft AGL would travel more than 1,000ft through the air, most of it horizontally.