Yes, for all the reasons explained above. Early morning before breakfast and before medication is the best. If you have to travel a long way for the test (which I do), be sure to be consistent. Don't get one locally at 8:00am then the next at another lab, further away, at noon - even if both are before brekkers and meds.
It takes me three hours to get to my blood draw lab and I do not have breakfast before the draw nor do I take my NDT. It is quite an ordeal because I absolutely need my breakfast before I can string two sentences together. I live in a remote place in California and all of my local labs closed down (well, one is still open close to a heavy duty prison 60 miles away but that is quite creepy!).