Small amounts of baking soda are highly unlikely to have any effect upon the body's pH. The kidneys are highly effective at regulating pH between 7.35 and 7.45, and a person with normal kidneys rarely falls outside this range (acute respiratory problems and ingestion of toxins are the major examples of times when this can happen). As a matter of fact, the kidneys do this by altering the production and excretion of sodium bicarbonate -- i.e. baking soda! Taking additional baking soda usually just causes the kidneys to excrete more sodium bicarb and causes the urine pH to rise.

Similarly, the transportation of oxygen is also very unlikely to be altered by baking soda. Though decreases in pH (more acidity) will cause hemoglobin to release more oxygen, this is generally a local effect caused by local tissue hypoxia. When an area of tissue is depraved of oxygen, it will enter anaerobic metabolism, producing lactic acid and lowering the local pH, thereby causing any hemoglobin molecules in the area to release more oxygen.

However, the level of oxygen delivery does not really determine the rate of malignant transformation, which is the first step toward cancer. That is determined by DNA damage, one type of which is oxidative damage. Though similar sounding to oxygen, oxidative damage in the body actually occurs from free radicals. Entire lectures in chemistry can be given on the topic of oxidation/reduction reactions, but suffice it to say that free radicals induce changes in DNA that can render that section of DNA inactive or overly active. If that section of DNA is a tumor suppresor gene or an oncogene (cancer-causing gene), then that damage can lead to cancer.