It depends on your age and how elastic your skin is now. It usually happens only when you lose a lot of weight. Since you most likely will not lose that much weight in a week (practically impossible) you probably don t need to worry about it.
No, I lost 40 lbs in about 5 months and no skin sag =P You would need SEVERE weight loss for there to be skin sag. As long as your working out while losing it, your skin will tighten up again.