Yes, Apple went with lithium-ion (polymer?) for some good reasons.
http://www.batteryuniversity.com/partone-12.htm
Interestingly, it is claimed that "cycling" or depletion isn't necessary for lithium type rechargeables, and there is no "memory effect" common with older nickel based cells.
(Though, the software may require this periodically for accurate indication/calibration!)
It also states that "priming" or a long initial charging isn't necessary for this type of cell albeit that manufacturers typically ship this battery with a 40% charge to allow for any self-depletion. That is probably consistent with the iPhone "out of the box".
If the charge drops too low, it will not be re-chargeable by consumer type equipment.