Answer:
Not if you eat the right amount.
Fat contains 2.25 times the energy of carbohydrates so when you eat fatty food you are probably eating a lot more energy than your body needs. Your body then stores this excess energy for later use.
It is best to just follow the council to minimize how much you eat unless you are extremely physically active.
However it is worth remembering that fat is actually a necessary part of a healthy diet and should not be cut out entirely. A person eating a healthy diet should be getting no more than 20 to 25% of their total calorie intake from fats and ideally these should primarily be unsaturated fats, for example olive, peanut, sunflower and sesame seed oils are all relatively high in monounsaturated and polyunsaturated fats, and low in saturated fats and so more healthy.