Here you go.
http://www.apple.com/support/iphone/service/faq/#warranty7
In short, no you can't keep your broken phone. "Swapping" is the idea and that's why they can sell you one for cheap. See details on the page.
Beat me to it bro.
Apple - 199. Drop in, swap out, pay up, walk out. AppleCare or not. Couldn't be easier.