We have been playing with throwing and flying the Crazyflie for a long time though we where flying it manually, this is a nice effect to do it with the barometer

. It definitely looks possible to do with the Crazyflie.
Do you observe much drift even when the Crazyflie is on a table or only when it is flying?
For flying, one low-tech way we have used to stabilise the gyro is to stuck some foam on top of it. The foam that is present in the Crazyflie box works well, I usually cut a cube of it and stuck it under the battery on top of the pressure sensor.
When standing still on a table, what we have observed with the barometer is big steps that are caused by people opening doors and windows (during the winter I could detect someone opening the entrance door of the building one floor bellow ...). I guess this can be solved by correlating acceleration and pressure information and ignoring steps that are only in the pressure and not in the acceleration. Though this work has not been started yet.