The phone will, generally speaking, but the battery is something made by another company, and Apple have no control over any variables in QC or lifespan.
This is incorrect I am afraid. Apple don't have complete control but would have a very firm grip on their supply chain.
Well of course they do, and Tim Cook is the acknowledged master of controlling the supply chain, but he isn't omnipotent, he has no overall control over every third-party's production line, so cannot vet every battery that goes into an Apple product, which was clearly shown with the issues surrounding Sony batteries spontaneously igniting in PowerBooks several years ago. When there are tens of millions of batteries being produced every year for iPhones and iPods alone, there are almost certainly going to be a percentage which will fail early, for whatever reason; that is a statistical fact, nothing is 100% perfect. Anyone expecting any product to be 100% perfect, flawless, and to last for many years without fail is deluding themselves. The home button on my iP4 is a bit flaky, this is a known issue, due to Apple changing the button mechanism for a quieter, softer click. They changed it back for the iP5, but apparently customers have complained about the 'new' button being too noisy!
What are Apple to do? Stick with a component that fails early, or stick with a component that doesn't, but gets complaints for other reasons?
Damned if you do, damned if you don't.