Does the noise of the AD9726 change when the output current is 0mA or 20mA?

Hi:

You need to be a little more specific. Are you asking about a single sided output from either the + or - Iout pins when the digital code is all zeros vs all ones or when you change the Vref / Rref to change the output current? The analog DAC output is differential such that the sum of +Iout and -Iout is constant, nominally 20 mA. Since the nominal mode of operation is expected to be using the output current differentially one can expect the noise due to the Vref (taken differentially)  will be minimum when at mid scale (both outputs at 10 mA) because it is common mode and will be removed differentially. Uncorrelated Nose generated by the individual DAC current sources will add RMS so looking single ended the noise will be proportional to the output current so at 0 current the noise (from the analog DAC current sources) will be zero. At full scale current the analog noise will be maximum. Looking differentially, the uncorrelated current source noise will be more or less constant as it is not common mode and will not be removed

Digitally induced noise (as well as quantization noise) will generally be constant regardless of the output current and a function of the digital activity i.e. number of bits changing.