Not if you eat high fats you daft twat.
A true Paleo diet is a very high fat diet, all from animal sources. Paleolithic Man was able to survive very well on a high fat, protein diet, from animal sources, and they didn't get fat. Up until about a 100 of so years ago, Eskimos, Laplanders, and Tungus peoples in Northern Siberia, all ate that diet, and had none of the modern diseases caused by the the modern high carb diet.