Answer:
This largely depends on the soda. Most sodas are slightly on the acidic side.
Coke, for example, has a pH level of 3.4. Freaky, right? Strong enough to slowly dissolve teeth and cause damage to bones over time.
The pH level of baking soda is 8.5.
In short, there is a reaction. It may not be noticeable when the soda is first opened, but it is definitely there.