What are the limitations of the aerodynamics modelling used in flight simulators?
Size matters here. Big aircraft have more inertia and take much longer to respond, but can equal out small-scale turbulence better. Your drone idea for training will not be representative of the big airplane at all.

Turbulence can be modeled quite faithfully - you just need to fly once through rough air, collect all the data and replay it in the simulator. The changes due to different pilot responses can be added on top without much loss in accuracy against a real flight.

Where models for airliner crew training break down is when the linear range of aerodynamics is left. Their post-stall and spin behavior is most likely not suitable for training, but that is not what they are designed for. Military aircraft simulators can even model the post-stall regime well, but need a lot of aerodynamic data, and most of that data is from wind tunnel models and not from real flight test.

What the simulation does is to plug the actual values of angle of attack, angle of sideslip, airspeed, power level angle and control deflections into matrices of coefficients and calculate the result from linear addition. That works well as long as the forces vary linearly of the flow angles, and correction factors will give you still good agreement with reality well into a stall. The coefficients are a mixture of CFD, wind tunnel data and flight test data. Gust loads can be modeled with Markov matrices which produce a realistic distribution of gust intensities, so even external, stochastic factors can be modeled faithfully.

I have less knowledge of helicopter simulators, and I would assume that flying near tall buildings can only be modeled in general terms, but not well enough to train a pilot for a specific location and weather condition.