Can someone die of acid reflux disease?

No. No, not gerd per se. Gerd can lead to barretts esophagus which can lead to esophageal cancer and ultimately death. Esophageal cancer is becoming more common and has a high mortality but is still relatively uncommon.
Yes but rare. As dr. Vinson noted, major concerns are longterm complications. However, depending the amount/degree of refluxing, there are certain subgroups that can have complications more directly associated with gerd. Some infants have respiratory complications and/or sid thought to be associated with gerd. Some adults may have significant lung disease and/or infection associated with refluxing.