Yes, you can make beer in a week. It will, of course, depend on the style you want to brew, and you don't have time for secondary, but 9-10 days in primary and a day of force carbonation is enough time for a drinkable beer.
You'll need a simple recipe for a low to moderate strength beer. High alcohol, dry hopping, and other post-fermentation additions are out of the question.
Expect the flavors to be a bit harsh and grainy, and the beer will still be hazy and yeasty, as eleven days isn't nearly enough time for the tastes to meld and mellow and all the yeast to flocculate, but if all else goes well, the beer should be fine.