I think this question may be better asked at biology.SE.
I have to cite popular science press here, but nevertheless, clearly the answer seems to be: no.
Peter Pressman of the Cedars Sinai Medical Center in Beverly Hills, Calif. and Roger Clemens of the University of Southern California School of Pharmacy explain. Food craving, defined as an intense desire to eat a specific foodstuff, is a common occurrence across all cultures and societies. These yearnings (...) are not linked to any obvious nutrient insufficiency.
From a more comprehensive take on this from the WSJ:
For decades, researchers surmised that food cravings were the body's subconscious effort to correct nutritional deficiencies. Longing for steak could indicate a need for protein or iron, according to this theory. Chocoholics might be low on magnesium or other mood-altering chemicals that chocolate contains, including phenylethylamine, a compound humans produce when they're in love.
But a growing body of research casts doubt on the nutritional-deficiency notion. After all, few people crave vitamin-rich green leafy vegetables and many other foods contain more phenylalanine than chocolate—including salami and cheddar cheese.
So the more cogsci.SE related questions might be about the complex cultural, affective, cognitive and neuropsychological factors (such as stress and social norms) that foster cravings for certain foods.