The air-driven gyro in a normal light aircraft AI needs to have some form of "vertical sensing" so that it can erect itself correctly when first starting The gyro's centre of gravity is below its gimbal's "rotational" centre (if you see what I mean) so that it hangs vertically when the gyro isn't spinning.
That's true as far as it goes. But when the aircraft is flying along in a straight line with an angle of bank on, the
gyro remains vertical while the instrument rotates around it. Thus I don't see how the erection mechanism would affect it, even after prolonged flight in that state.