In general not immediately, you cannot eat enough of most foods to kill you at any one time. There are some foods that can kill you even if you eat just a bit, e.g. polar bear liver.
It is an interesting point to note that carnivores (meat eating animals) tend to only eat herbivores (plan eating animals). The reason for this in not just that carnivores tend to be more vicious but also that toxins build up as you go up the food chain. Say there is a bit of a toxic substance in a particular fruit but the bird that eats it doesn’t eat enough to do itself harm, well the predator (say a ferret) that eats those birds will eat a load of them but still not enough to get too much of the toxic substance. If something were to come along and eat loads of the ferrets it would get a much higher dose of the toxin and maybe even become ill and die.
And of course everyone has heard of poisonous mushrooms and the like.
Food can kill you though. It can kill you through blood pressure, heart disease, cholesterol and diabetes.
But there are other ways it can kill you too. It can kill you because of its nutritional content. You can eat load and loads of food but still die of malnutrition even though you haven’t been starving. Too much of the wrong kinds of food can kill you.
This doesn’t really happen much not because we know a lot about nutrition but that is how sailor got scurvy. Sailors would not eat fresh fruit or veg on long journeys as most didn’t last. They had plenty of food but they were malnourished as they weren’t getting enough vitamin C. Nowadays most cases of scurvy in Ireland happen in college students living away from home! But I’m guessing those aren’t biology students coz they should know better!
There are also stories of trappers dying of malnutrition even though they were gorging on rabbits. The reason for this is that though the rabbits could fill them they did not provide enough nutrient to live on.
Food can kill you due to what it has: toxin, parasites, bacteria, poisons etc.
Food can also kill you because of what it lacks: certain vital nutrients.