Other Warnings
Do not consume alkaline water with any medicines, supplements, or other additives. The alkaline water is reactive, and can form potentially dangerous by-products when mixed with a drug or other chemical compounds.
You should store ionised water in sealed glass bottles rather than plastic bottles, because it is reactive and can react with some plastics. It also reacts with the air and loses its ionisation if it is left exposed (of course, the alkaline minerals remain).
Others say that alkaline water helps:
http://www.alkalinediseasecure.com/acid-reflux/
From what I've read, it seems that alkaline water may help but only where you in fact have High Stomach Acid GERD. Where you have Low Stomach Acid GERD, it appears that alkaline water may make the problem worse.
So, if you've determined that you have High Stomach Acid GERD, which you can do by doing the HCL test, then you may want to try alkaline water. When you do, make sure you pay attention to how you feel and how your body reacts to the alkaline water.