The human stomach can hold approximately 4 L of food. Various mechanisms, such as vomiting will prevent further distention. 4 L is about 25 shredded carrots, so you will probably be sick if you eat this amount all in once.
Going further into the nutritional value of carrots. Carrots are a good source of β-carotene, which can be converted by the body into the Vitamin A. Vitamin A is toxic in high doses, but in form of the β-carotene, the body can maintain the required levels of vitamin A, hence preventing hypervitaminosis. The excess of β-carotene stored in the fat tissues. The side effect of high intake of carotenoids is the yellowish skin colour, which quickly gets to normal when you stop consuming high amounts of beta-carotene.
Adequate intake of carrots is good for you, 25 carrots at once will make you sick.