Quadrotor flight controller and actuator dynamics
All of the papers I've read on flight controllers (disclaimer: I haven't tried to implement one) appear to use a similar method for control - a PID controller wrapped around each axis of control, where the outputs are distributed and summed as motor pairs. Each motor's control signal is a sum of those PID outputs, with the sign of the output varying by motor position. 

So, if that's the case, then no, there is no dynamic accounted for in the flight controller. The flight controller sends the reference to the PID controller, which needs to be tuned. This is one of the drawbacks of PID control - you need to tune it. Tuning can be a very time consuming process. 

Fortunately, there are procedures written to tune PID controllers, but just because a method exists doesn't mean it's easy to do. 

There seems to be an auto-tune feature for some flight controllers, but again, the tuning needs to happen because the thrust dynamics are not taken into account. 

One motor with a large prop and the same motor with a small prop are going to produce different amounts of thrust at different speeds. That is, even if you know the BLDC motor dynamics, the thrust you get from that motor (which is really what you care about), still isn't accounted for because you haven't modeled the effects of the prop. 

Tuning the PID gains is how this variation is taken into account. The gains are larger or smaller, as needed, to account for response time in the motor/prop combination.