Does skipping breakfast before working out burn more fat?

Yes, BUT...
You will burn more muscle as well.

Explanation:
Your body stores carbs and fat for energy. Carbs are stored in our muscles and liver. They are a quick and easy source of fuel. Fat is stored all over our bodies and is a much slower source of energy. When you sprint, you are burning 100% carbs, and no fat. When you do endurance exercise, you are burning some carbs, but also a lot of fat.
While you sleep at night, your body will burn mostly fat because energy is in low demand; however, you will still burn a lot of carbs during those 8 hours. If you exercise without refilling those carb stores, then your body will look for another source of fuel. That is when you will start burning muscle (protein).

Solution:
Eat SOMETHING before working out. Breads and cereals are excellent because they are easy, but any carbs will do. Remember, you don't need any protein until after the workout.