It depends if your body has transitioned to burning fat. This normally takes about 3 weeks of being on a low carb diet. People who are not, will "hit the wall". Even if you are on a low carb diet, it depends on how hard you're going. Having carbs while in a competition situation would give you an advantage. Fat burning works at a slower pace than carb burning but can continue much longer.
Out of curiosity, when you say "hit the wall" what do you mean? Actually going hypoglycemic and passing out?
On a related note, I highly do NOT recommend going to an all-you-can-eat Indian buffet and then running a few hours later. I had 2 plates piled with food and then 2 bowls of rice pudding and some galub jamun (a traditional dessert).
I had indigestion pretty bad but I tried my best to keep it under control. I felt like I couldn't make it but I just kept pushing myself and made the whole 5 miles. I felt dizzy/faint at the last mile but my heart was at 187 (this is about normal for me around that time).
I've had this happen before when I ate a lot of pizza with hot sauce. I eat a *lot* of spicy food so it usually doesn't bother me but I should probably keep it in mind next time I run ;)