Measuring AC current: Is true RMS needed for a clamp ammeter?
Yes.  When you have non-sinusoidal signals and want to measure their "real" voltage or current, then you need to do true RMS calculations.  Ordinary voltmeters and ammeters take the average of the absolute, assume the original was a sine, then scale the result to provide correct RMS for that (sine) case.

Note that if you want to find real delivered power, just having true RMS of the voltage and current separately still isn't enough.  If you know the voltage and current have the same waveshape and are in phase, then you can multiply their RMS values to get real power.  With arbitrary voltage and current waveforms, the only way to get real power is integrate the instantaneous product of the voltage and current over a whole cycle.  Unfortunately for you,

Ave(Volt(t) * Curr(t))

Is not the same as

Ave(Volt(t)) * Ave(Curr(t))

Physics can be so inconvenient at times, especially when you're on a budget.