unless of course the water scavenge jet pumps are blocked by ice. If they are blocked on the suction side, the fuel jet will be undisturbed so there will be no indication that the water scavenge pumps are not working.
The Boeing manual states
You should get a fuel sample from the sump drain valves
before and after you do the refuel procedure. A large
quantity of water in a fuel sample that you drain from
a tank before refueling is an indication of a blocked
water scavenge jet pump.
So the only indication of the jet pumps not working is water accumulation.
Exectly that is the reason why those are jet pumps, and no impeller type pumps, if they fail they do not produce any secondary failure like blocking of an electric motor and setting of a circuit breaker or cause overheating etc.
The effect of those pumps is, that you don´t have a solid block of ice in the tank, but a slush of fine ice crystals.