To answer this question simply, it is not necessary to take Pre-Workout Supplements on an empty stomach. If you have recently eaten a meal, a pre-workout will still be effective and will assist your performance during your training. The main difference between taking a Pre-Workout on an empty stomach rather than after eating a meal will be the duration it takes for that product to take effect.
If you have an empty stomach, a Pre-Workout will be able to absorb much quicker and the ingredients will enter your bloodstream rather rapidly. As a result, the benefits of the product, whether that be energy, focus, strength or muscle pumps, will hit you far quicker than if you took a Pre-Workout when you have a meal in your system.
If you have recently eaten a meal, it may take an additional 15-30 minutes to feel the effects of a Pre-Workout, by the time it is absorbed. This does not mean it is less effective, it simply means you need to consider this when planning what time you wish to train. If your Pre-Workout will kick in later than expected, use the extra time to warm up, stretch or socialise! That way when it kicks in, you can focus 100% on your training.