Sorry, but baking soda does not, and can not, change the pH of one’s body. It cannot even change the pH of one’s intestines.
The reason is quite simple. The stomach is designed to maintain a very low (acid) pH. It must do so for two reasons.
The first is digestion. A low pH causes proteins to unfold, and thus to be accessible by digestive enzymes. Plus, those digestive enzymes are optimized for working in a low-pH environment. Too high a stomach pH means a bad digestion (this is actually a stomach disorder that may occur at advanced age).
The second reason is killing bacteria. Even if you only drink water, the stomach will secrete acid. After all, in our previous natural environment water could never be trusted to be free of bacteria and parasites. Therefore, it was downright essential for our survival to make sure the stomach is acid at all times, even if you only drink some water.
Now of course, if you suddenly drink a whole lot of water, the contents of the stomach will become less acid. That’s just simple dilution. So the stomach responds by closing the exit towards the intestines (I don’t know how that exit and its muscle are called in English). The exit remains closed until the stomach has released enough additional acid to restore its internal pH.
For the very same reason, consuming baking soda is useless. The only effect is that it closes the exit from the stomach to the intestines, and that it forces the stomach to work harder and secrete more acid to restore its internal balance.
Taking baking soda does result in a reduced acidity inside the stomach. But only inside the stomach, not in the intestines, and certainly not in the body. And, this reduced stomach acidity lasts only for a limited time, until the stomach has released enough HCl to undo the effects of the baking soda.