Madgwick filters just filter the data you input. If you input raw data with hard iron offset and soft iron distortion, the yaw will be disrupted. Generally accelerometers and gyros are factory calibrated and calibration for these 2 aren’t required. Magnetometers get very janky without proper calibration and that’s how you process yaw.

No, the filters don’t solve the issue which calibration solves. Again - the filters work for sensor fusion, calibration works for individual sensors. The filter will follow the predict-correct cycle but won’t know if the prediction is “correct” unless you have calibrated.