DL's can give an extremely musculer core structure of 360 degrees around the mid-section. And when including serious heavy ab work, an even more impressive and strong mid-section. Fat (a gut) is just that, fat. You will get that from daily intense over eating workouts of too many not needed calories.
If you work the DL with serious intent, than you will achieve a very well developed upper body, including a wide muscular back. Which in return will make your waist look even smaller. So DL's are a win win situation. Good Luck.