Average atmospheric pressure at sea level is 14.7psi. That means that the force the atmosphere applies over 1 square inch of surface area of any object is only 14.7psi.
The diameter of the Saturn V (which hundreds of people have watched lift off in person) is 33 feet. That means the area of it's base would have an area of 123,163in2.
So, the most force the atmosphere could apply to the base of the Saturn V would be almost 1,810,500 pounds. The Saturn V weighed 6,200,000 pounds all up.
So even if there was no atmospheric pressure acting on the upper parts of the rocket, there is no way that the atmosphere could even lift the rocket, let alone accelerate it to speeds approaching 1.5 miles per second.
Edit: For the sake of curiosity, the difference in pressure between what is acting downwards on the Saturn V (from the air on top), and what is acting upwards (from the air underneath) is 22,615 pounds (as best I can figure). What this means, is that if the Saturn V weighed less than 22,615 pounds, it would float!