I have a broken iPad that is being replaced tomorrow, is there any chance I could still keep the broken one?
As a former Apple employee, I can tell you this is not possible. Apple will use undamaged parts from the one you return to create refurbished units that are sold online, as well as service replacements for Genius Bars. If they shipped you the replacement in advance, you could technically just not return the damaged unit, but you will be charged for it after a certain number of days (I believe 30).

If your sister wants a good deal on one I would keep an eye out on the refurbished section of the Apple Online Store, or on Craigslist or eBay.