Short answer: no. pH is very important in skincare.
Too alkaline and your skin can experience drying, dehydration, and inflammation. If the pH is too acidic, you may experience breakouts, irritation, and burns.
pH of 1 is acidic while pH of 14 is alkaline. Baking soda has a pH of about 9. As a reference point, your skin is roughly a pH of 5.5. This pH keeps the skin moisturized with healthy oils & protects itself from viral & bacterial infections.
The top layer of your epidermis is called the moisture barrier, and this keeps your skin supple & moisturized. The moisture barrier is protected by a film called the acid mantle. When you use products like baking soda, your skin becomes too alkaline, and its natural acid mantle & moisture barrier are damaged. While you may not experience any immediate issues after using baking soda, you will experience symptoms like inflammation, dryness, redness, and/or breakouts after prolonged use.
Sources:
https://www.sciencedirect.com/science/article/pii/0738081X9500102L?via%3Dihub
http://europepmc.org/abstract/MED/1980979/reload=0;jsessionid=fILBJuhSpjuSVCb7W4kK.0