I had the same trouble wraping my head around this issue.
The straight forward explanation is: **it does not matter if it is an ADC or a DAC**. In the end both are a sampled system with the same nyquist properties.

The ADC appears to be easier to understand.
Assume you have a distorted signal with infinite bandwidth.
This signal is then sampled without a nyquist filter and with a finite sample rate by the ADC.
If any of the harmonics is outside of the sample rate's nyquist frequency, it will show up as aliasing in your band.

The same is true for the DAC.
Assume that a DAC is converting a quantized but otherwise pure sine wave.
Without the reconstruction filter, the output spectrum is periodic.
There is one peak at the sine wave's fundamental frequency which is repeated every fs/2.
If this signal (which is not yet low pass filtered by the reconstruction filter) is then distorted, you will experience the exact same situation as with the ADC. Namely, higher frequency aliases which are still present are distorted down into your band of interest.

To make it clear:
Assume your DAC is ideal without distortion.
Assume you apply a reconstruction filter at the DAC output.
Assume this reconstructed signal is then distorted by a nonlinear amplifier.
You will **NOT** have aliased harmonics.

However:
Real **RF-DACs are already non-linear and therefore already distort the signal before any reconstruction filter can remove the aliases**.