Sort of. While there is still plenty of air at 40,000 feet the problem is that the surrounding air pressure isn't enough for your lungs to efficiently work. Hence the need for supplemental oxygen.

When the masks drop, the oxygen to the masks is delivered from either a system of high pressure bottles or generated from a chemical reaction. If there is an emergency requiring the use of masks, the flight crew will descend rapidly to an altitude where people can breathe without the use of supplemental oxygen, say 10,000 feet or so.

I asked a first officer about the plastic baggies on the mask and he told me that the reason they are there is because the oxygen system on the aircraft is fixed flow (meaning its on all the time). To help regulate the flow of oxygen, the baggie can collect oxygen when the passengers are not breathing in and release the collection oxygen when they are breathing in. He said that if everything is working right with the emergency O2 system then the bags will typically not inflate or only inflate part way. He also said that they have a few minutes to get down to a breathing altitude and that in all of his flights he has never had the masks deploy.