newton's third law says yes, at least to some extent. unless the barrel is perfectly aligned with the platform's center of gravity, it will be deflected (at least a little) before the projectile exits. and it's not trivial to hold a quadcopter or fixed wing craft steady enough to aim precisely in the first place.
Do you need to aim steady or do you only need to fire precisely at the right moment? For example, TOWs using a top-attack EFP warhead don't "aim steady" either, they just detonate at the right moment.
I assume that the time spent in barrel is more or less constant compared to the other variables (such as angular velocity or angular acceleration of the barrel around the time of firing) and can be considered a fixed time delay in the system?