Yes, you can. When you have a white coating on your tongue, usually accompanied by the same on the insides of your cheeks and even in your throat, you have a condition known as oral thrush. Thrush can develop in men, women, and children of all ages and is especially common in babies, the elderly, and those with immune disorders. Individuals who take medications that might mess up the balance of yeast/bacteria in the mouth, like inhaled steroids, are particularly susceptible as well. You may need to take oral antifungals, rinse with antifungal rinses, and alter your diet until your condition clears up.
Please see these two other questions that people have asked for answers on yeast infection in the mouth or oral candidiasis.