It's a function of the speed of the plane, the shape of the ice, and the amount of reduction in inlet size.
There will be different effects from different designs but, not enough inlet will guarantee loss of ability to produce power.
That colgan plane that went down had big time inlet icing and, when they realized that they were stalling, firewalling the throttles caused the engines to make less power. Some witnesses reported popping noises which likely means they had compressor stall from one or both as well.