Does position error from accelerometer still build up quadratically when using Kalman filtering?
No amount fo filtering can correct a contant error that is inherit in your input data.

Assume you are in rest, but your accelerometer gives a reading of a very low constant value X (its error). No amount of filtering will change this. 

Integrating this X over time gives your 'speed' t * X, which increases linearly.

Intergrating this speed over time gives your 'position' (1/2) * t^2 * X, which grows quadraticly.