I'm being picky here, but an averaging meter will just display zero, when given an AC signal with no DC component and is what a meter does when set to read DC.
There are different types of non-true RMS meters:
An averaging non-true RMS AC meter will high pass filter the signal first and rectify it, before taking the average value, which will be less than the RMS value of a pure sine wave, so it will multiply it by a correction factor.
A peak detector will high pass filter and rectify the signal, before taking the peak value, which will be more than the value of a pure sine wave, so it will be divided by √2.
In other words, in a true sine wave meter, the measured waveform is assumed to be sinusoidal and peak or average value is scaled to reflect this.