Wouldn't the back-EMF drop to zero and resistance drop to only the actually value across the coils, therefore causing the current to spike up, possibly limiting the ability of the generator to maintain the voltage, causing a brown out?
Pedantic, I know...
No, an ice chunk jamming in the props is taken into account when designing the system.
Worst case, your protection trips and shuts off the motor.
As an example, one vessel I worked on had a "boost" module for her generator exciter for exactly the scenario you described.
If the exciters couldn't handle the load, the boost module kicked in for a up to a preset time.
The timing on the motor protection would be set a bit shorter, so either the ice chunk came out and the motor began to spin normally, or the motor tripped off before the boost module shut off.
That was an older vessel, other vessels will probably handle it differently, probably just current limitation in the propulsion drives/trip off the drives, but ice jamming will be considered in the design if it's classed as an ice breaker.
Conventional propulsion vessels classed as ice breakers will have some sort of design consideration to deal with it as well, probably either a clutch designed to slip at high torque or sacrificial "shear pins" like a snow blower.