The 1V range from 3-4V isn't the problem. The IC regulates by comparing the output voltage with an internal reference voltage, so as long as the input stays within spec (some unpublished minimum voltage to a max of 50V) and below your desired Vout (this isn't a buck/boost converter), you should be fine. It's the minimum voltage requirements are worrying. Your desired operation from a single coin cell is really a special application, and, as Madmanguruman said, it looks like this IC was made for much less imaginative applications - boosting a 5V supply.
Since your users might be tempted to stick in an alkaline battery or a dead battery, why not use something that's designed to work with a lower voltages? Linear Technology's LT1308 switcher will work down to 1V, and has a switch current of up to 3A, so you should be able to get 15V at 250mA out of it.
(Disclaimer: I like Linear products; I go to their site first to look up stuff like this. I didn't compare with other manufacturers, but you should.)