Re pitot icing; the principles of pitot operation is that air does not flow through the tubing, the system captures a pressure. There are some types (probably used by Airbus) which allow a small calibrated leak, but downstream of the ‘leak’ the systems’ operation are essentially identical.
A change in pitot pressure (erratic IAS) could occur quite quickly if an ice/water accumulation reduces the effective diameter of the tube, particularly with the ‘leaky’ systems. Diagrams showing the types of pitot and a range of disruptive mechanisms are shown in www.sae.org/events/icing/presentations/2007s30duvivier.pdf
An indication of the atmospheric conditions, icing type, and rate of icing can be seen by comparing the events of unusual engine icing and TAT probe icing – http://airs-icing.org/AIRS_II/AIAAReno2006/AIAA-2006-206-739.pdf