Well, technically you could obtain DNA from a stool sample as cells from the lining of the stomach are shed and adhere to the stool. The problem is that the odds of a an intact stomach cell surviving 2,000 years burried in the soil is next to nothing. Otherwise the best you could do is find undigested remains of food in the stool and do a DNA on that to find what the person ate. Man, this was such a nasty post. My nastiest yet. Sorry.
It sure beats drinking water and dying from explosive diarrhea from cholera, or a stomach full of water-borne parasites. There is a good reason why people drank light beer back then. I read somewhere that Oxford students in the 1800s used to get over a gallon of beer a day as rations. Of course, it was only 1% alcohol, so you ain't really getting drunk on that.