First, is this the correct way to measure PSRR?
It is a method of measuring PSRR but, if you are trying to find the PSRR of an amplifier under extended conditions you will come unstuck. This is because you need to use the amplifier's data sheet and look at the graphs for +PSRR and -PSRR.
If you tested one unit and it looks good that doesn't mean the next unit will look anything like as good. Hence, you do a design study on what you might expect under typical to worst-case conditions
Would using the line regulation of the regulators be a more accurate
way to check how the output reacts to the AC noise?
I would probably start at this point and examine the data sheets of the regulators then, knowing what input voltage perturbations are likely, I would estimate the type of level and frequency range I might see at the output. Then I'd use the data sheet of the amplifier to see what effect the regulator's output voltage fluctuations have on the amplifier's output signal.
If this way is correct how do I calculate the overall PSRR of the
stage since the op-amp and the ADC each have their own PSRR value.
The problem you face with multiple stages of amplification or signal processing is that sometimes you might get opposing PSRRs from each stage that might give a false impression of high-quality. And, of course, the data sheets will not tell you if that might happen.
However, in an amplifier chain, it's usually the front-end chip that is handling the lowest level signal so, analysis of the front-end circuit may be enough to give you confidence in future real performance.
