Yes Ginger ale can help relieve an upset stomach and has been used for years to treat upset stomachs.
Drinking Ginger Ale can also lower the chances of your throwing up which happens a lot during an upset stomach.
Ginger Ale can make your stomach more gassy though if your stomach is already filled with gas so if you have a lot of gas on your stomach it's not recommended to drink Ginger Ale.
And if your stomach is upset sometimes it's better to go ahead and throw up to make your upset stomach fill better but if you want to you can drink Ginger Ale for the upset stomach.