From my experience...Depending on how the order was placed (STAT or routine), the reason for the CT (emergent or routine), and radiologists staffing at the facility it can take anywhere from 30 minutes to 36 hours typically to receive a CT result.

Depending on the severity of the heart burn and some nutritional factors there are a few potential complications. You could possibly develop ulceration of the stomach, small intestine, and esophagus which are spots in the lining of those areas where the stomach acid erodes through the tissue, often causing bleeding and discomfort. This disorder can potentially manifest in the form on gastric pain, red vomit, or black feces.
Another possible complication is Barrett's Esophagus, which is when the cells of your throat essentially mutate into cells similar to those in your stomach in an attempt to stop the extra stomach acid from further damaging the tissue of the esophagus. Developing this disorder puts you at higher risk of esophageal cancer. The most severe possible complication is a GI hemorrhage, that is when the ulcers in the lining become so large that there is an uncontrolled bleed, this is a medical emergency. If you vomit blood, or have multiple black or dark red bowel movements in a row, you should see a doctor. If you experience either of those symptoms and feel dizzy, fatigued, or lightheaded, you should go to the emergency room.

Short answer is yes, for most people. Long answer is also yes for most people. The only patients that it is POTENTIALLY unsafe for are those with severe kidney disfunction. Before getting a CT with contrast, typically labs are drawn to see what your baseline kidney function is. Once the doctor has the results they can make a determination as to whether or not risk outweighs the benefits of the superior imaging results. If kidney function is is low, meaning the lab values result as high, numerically, the physician may opt for a CT without contrast. The images are less precise but can still give a general idea of the anatomy. Some side effects of CT with contrast are a warm feeling, like you have to pee when the dye is injected (this goes away within a few minutes typically), a possible allergic reaction, and typically a temporarily decreased level of kidney function. The are a very common and useful diagnostic tool, concerns should be discussed with your physician though.