Does the human body keep track of sleep overages and deficits over time? If so; is your body capable of remembering these over the span of a lifetime? If so; would this mean that one could "stockpile" sleep?
Yes and no. You can not build a "stockpile" of sleep. However, your body can accumulate "sleep debt." The amount of sleep each person needs varies. In addition, how your body addresses it's sleep debt depends on the circumstances.
Let's say, for example, you need 8 hours per night. If you have zero sleep debt, you will not be able to sleep more than 8 hours. But if you sleep for only 7 hours one night, you add 1 hour to your sleep debt. If you do this Sunday through Thursday night, you will have 5 hours of sleep debt.
The catch is, most people can not relieve themselves of more than about an hour of sleep debt per night. So, even if you sleep for 10 or 11 hours on Friday and Saturday nights, you would most likely not make up for your lack of sleep all week. The quality of sleep diminishes with each sleep cycle, so those last couple of hours aren't nearly as effective as the first few.
Most people are carrying around sleep debt. In fact, it is healthy to have a small amount of sleep debt (say, 5-10 hours). If you have too little, it is difficult to fall asleep at night. If you have the right amount of sleep debt, you should not feel tired during the day but it should only take you 10-15 minutes to fall asleep at night.
However, generally speaking, there is a cap to the amount of sleep debt you can accumulate. If I remember correctly, it is at about 50 hours or so. The average person is walking around with about 25 hours of sleep debt or so. Many sleep specialists believe that a large portion of auto accidents have a root cause of lack of sleep, but it is difficult to accurately measure this. 50 hours of sleep debt has a similar impact to your ability to function as if you had just finished off a couple of beers.
There's an excellent book on the subject called "The Promise of Sleep"