No, in general. When we exercise, our body works harder to pump blood to our muscle cells that need more oxygen and energy. How much depends on how hard you are walking/exercising. Similarly, when we eat, blood is sent to the stomach to transfer the food energy from our stomach to other parts of our body. So if you eat and exercise at the same time, you are sending blood both to your stomach and to your muscles. This might create a conflict but only if you are exercising very intensely, like if you were panting hard. For example, marathon runners usually will take on some very simple sugars at the end of their race because these are digested quickly. But they are still racing hard, so fundamentally it is not unhealthy. The other possible effect is that having food in your stomach while exercising might mean you can feel it bounce around – not pleasant at all!
Tim is right. Your digestive system has a really rich blood supply necessary to absorb the nutrients in your food. When we are exercising our bodies release various signaling molecules that direct our breathing to become deeper and more frequent and our hearts to been more. Blood is directed mainly to our muscles at the expense of blood going to the digestive system. One of those signaling molecules is adrenaline and this is why when you’re nervous or excited you can have “butterflies in your tummy” and not feel like eating.
In practice: It would certainly not be advisable to eat a meal and walk but snacking is ok!
Indigestion and light headedness are not a fun combination.