I am not sure if it has been mentioned before, but in addition to the 2 fuel pumps in each main tank, there is a pump bypass valve in the left and right tanks that allow the engine driven fuel pump to suction fuel from the tanks in the event the boost pumps are not working. I believe that this situation would be highlighted by a level B ENG FUEL PRESSURE warning which includes an audio warning.
Additionally, if the boost pumps were not providing flow, they would also give a similar LOW PRESSURE warning. And if all that ice was heading down to the engine, I am sure that the FUEL FILTER clogging warning would have come on.
Even if the crew had no time to deal these warnings, these should have been recorded and the data should have been correlated with system faults in the central maintenance computers. I am sure that these computers have been interrogated already and we would have heard about these problems.