Charcoal is almost entirely made of Carbon... So you can measure the ration of C12 to C14. However, the theory behind carbon dating ignores potential variables that could effect it's acuracy. Kind of like if I measured my nephew's height over a year's time, then calculated how long it would take for him to double his size, and then "scientifically" calculated how long ago he was two inches tall. (That's a hyperbollic analogy, but you can see it makes assumptions and ignores variables that effect the acuracy of employing that method.)
Radiocarbon dataing is not very usefull in actually determining the age of material with much degree of certainty... Despite this fact, it's still employed as a propoganda tool knowing most people don't know any better.
It depends on what degree of "certainty" you are looking for. The only "variable" that affects radiocarbon dating directly is the variation in the amount of C14 being formed in the atmosphere by radiation from the sun, which is affected by the variation of the "solar constant". Cross-calibration of radiocarbon with dendrochronology takes care of most of that error for "more recent" dates (out to -10-20,000 years or so).
Most people who think carbon dating is "propaganda" are biblical creationists, trying to stuff their religion down the throat of science.