pingswept is right about the amplification, but he cuts a few corners. First, if you amplify a 0V-5V signal, the amplified signal range still starts at 0V! We'll need to fix that. The i-Snail is self-powered, which means it needs a minimum current to be able to output a voltage. So at no current the voltage will be effectively 0V, but it's possible that the lowest effective output voltage is, say, 5mV. The datasheet doesn't say. For the given sensor that would mean a 50mA primary current.
To amplify this low kind of level you need a rail-to-rail input-output opamp. A 100x non-inverting amplifier would amplify the 5mV input to 500mV. That's still too low to drive the transistor, but we can use a comparator to compare this with a threshold of, say, 100mV. Many comparators have open collector outputs, but those can often sink less than 20mA, so you'll want to drive the NPN with the comparator after all.
Alternatively you can skip the amplifier and directly input the i-Snail's signal to the comparator, and set the threshold to 5mV. Keep in mind however that this will be near the comparator's offset voltage, so you may have to trim that. It also depends on the minimum voltage the i-Snail delivers or the minimum level you want to detect. In the given example of 50mA that would be 6W at 120V AC.