They not only used wood, but llama dung for fires. I wonder how much C4 ended up in the food via their dung, just from the smoke and air rising from the fire, as it would be rich in it.
OK, first: food is rich in C4. Food is made from carbohydrates, which as the name suggests is made from Carbon, and the amount of C4 in the carbon is homogenous across compounds.
So the answer to your question is: insignificant amounts of smoke occur in fire-cooked foods, and the C4 composition wouldn't be affected anyway.
https://en.wikipedia.org/wiki/Inca_agriculture
They not only used wood, but llama dung for fires. I wonder how much C4 ended up in the food via their dung, just from the smoke and air rising from the fire, as it would be rich in it.
Still a neat way to try to validate diet.