If you let a lithim-ion battery drain completely you will shorten its life. Their most efficient use is frequent topups (which is handy because that's how they mostly get used anyway).
Memory effect doesn't exist on these types of batteries but they will degrade over time.. that's unavoidable. You should get at least a couple of years out of it though.
I fly RC electric planes and have used Li-Ion and Li-Poly batteries for years. A typical power setup on one of my planes can pull anywhere from
10 to 30 amps! When you're working with power potentials that can easily kill you, one takes due care to learn about the technology intimately.
Draining Lithium batteries pass their low threshold (or "low voltage") point can, indeed, ruin them beyond repair. However, the firmware will stop drawing a significant pull on the battery in order to protect the battery from entering this state. Attempting to re-charge a damaged Lithium battery can result in a fire, so you can rest assured that the hardware manufacturers have this notion foremost in their mind.
Draining a Lithium battery "completely" does not imply that the remaining voltage in the battery has gone below the low voltage threshold. Rather, it implies that the lowest safe voltage (and remaining milliamp storage capacity of the battery) has been encountered. We can presume that the designers have allowed a "reasonable" amount of time for the battery to remain in this state before falling off into the dangerous low voltage point.
If the iPod designers routinely allowed the cut off point (the alarm notification in the iPod that instructs the user to re-charge the battery) to be the point where actual damage was beginning to commence within the iPod battery, not only would it be a bad design decision, it would be a safety hazard as well.
Lithium batteries don't suffer from reduced performance or the "memory effect" that plagues Nickel-Cadmium battery technology (which are rarely encountered in portable media anymore these days due to their size and weight), but one limitation of Lithium based batteries is that there is a set of "life cycles" that will determine how many times that the internal material will accept and provide electrons. While frequent charging doesn't harm a Lithium based battery, each charge does shorten the life cycle a bit.
The general prevailing notion is that if you're going to charge, you might has well make a full use of a charge instead of merely topping them off. It's a simple decision based on the economy of maximizing the life cycles. As the end of the battery life is encountered, the capacity of the battery will start to diminish and will eventually fail altogether.
Also, consider the notion that the life cycles of these batteries are on the scale of several hundreds (if not thousands) of times. By the time that the battery has truly been used to full capacity, the iPod model will have stepped to the next generation of its release.
-joedy