Is power rating of transformer determined by input or load?
When you clamp a current transformer around a current carrying wire it would be totally expected that the current through the wire to the load wouldn't drop hardly at all i.e. the current in the wire would remain at least 99.9% what is was before the CT was clamped around it.

This means that the extra volt drop in the wire is going to be micro volts or a milli volt at worst case. So you have a wire carrying 12A passing through a CT and the CT primary (yes it's a still a primary winding) sees maybe 1 mV.

That's a power input to the CT of about 12 mW. That would normally be dissipated in the CTs burden but now you have a circuit instead of a burden BUT it will still only receive 12 mW of power.

Is that enough for a raspberry Pi? 

No.