Fronl1ne,
The RAT can be deployed automatically if hydraulic pressure fails. That is achieved by the total 'system' sensing a total loss of hydraulic pressure or a loss of all engine power.
In the case of iced-up pitots, the system would not 'know' that ice was causing erroneous readings. That is to say, the aircraft systems would need to be 'told' that the sensed 'q' was not to be trusted, because of ice.
But how could you tell if ice was causing the data to be unreliable? The systems would simply take the 'q' reading as correct, even if it was not.
It's difficult to imagine, therefore, how an automatically deployed standby pitot system would operate.
Maybe the engineers on this thread could expand on this.