Would an EtG or EtS ordered on the same specimen with a cut-off of 500 ng/mL at this time help differentiate between the cough syrup in the morning and a couple of beers the night before?
No. There are too many variables, and too little science, to draw such conclusions.
Since he did provide a history of having had a couple of beers the night before, should I verify this a positive test ? If the 0.02 could be due to the cough medicine, would I verify this differently?
There is no MRO role for interpretation. There is in particular no exploring for alternative medical explanations for the result. With alcohol, the result is generally reported "as is." Also, if alcohol is being tested as a measure of impairment, urine alcohol is a bad tool because it doesn't correlate well w/the worker's alcohol at the time he or she is tested. If your employer/client is pushing you to interpret whether the result could have been caused by Nyquil use the night before, I think you could respond that it is unlikely but not impossible.