Thought Experiment: If you fell out of a plane at 36,000 ft (11km), would the additional air pressure from falling allow you to breathe? Imagine you fell out of a plane at 36,000 ft (11km), roughly cruising altitude, with a parachute. If you deployed your parachute immediately, you would be stuck at high altitude with no oxygen, and considering oxygen at 36,000 ft is roughly 25% of oxygen at sea level, you'd quickly lose consciousness and suffocate.
Now if you waited to deploy your parachute, you'd rapidly reach terminal velocity for that air pressure, and if you fell with your mouth open, basically, would the additional air pressure from all that air you're falling into compress the air into your lungs sufficiently to reach or exceed normal breathing pressure? So in theory could you just spend the first few miles/km falling and breathing, and then deploy the parachute once you pass into breathable air?
 A: Here is a very rough calculation of the stagnation pressure.  At standard conditions, the density of air is roughly 29/22.4 gm/liter, or 1.3 kg/m^3.  At 11 km, the air density is on the order of about 0.2 times this, or 0.26 kg/m^3.  Assuming that you are falling at a pretty high velocity of about 100 m/sec (328 ft/sec = 224 mph), the stagnation pressure at this velocity is $\rho \frac{v^2}{2}=0.26\frac{100^2}{2}=1300\  Pa$.  This is roughly 0.01 atm above the ambient pressure of roughly 0.2 atm at 11 km.  This is consistent with what we calculated in the comments using Mike Dunlavey's approach.  So the conclusion is that the higher pressure resulting from falling through the atmosphere at 11 km (i.e., the added pressure at the entrance to your nostrils) would represent only a tiny fraction of what is needed to give ground-level pressure.
A: You will have more problems on your hands if you jump from that altitude without a oxygen mask. Assuming you're in a plane which was initially airlocked at sea level pressure, the moment you open the door, the sudden decrease in surrounding pressure will force out all air inside your lungs. This sudden decrease in pressure inside your lungs, will cause the remaining air to almost freeze. When you normally breathe in, the diaphragm contracts, moving down, while it relaxes and moves up during breathing out. If all the air is squeezed out, the diphragm will flex upwards too much, causing fatal problems on the way down, including suffocation to death.
