While this makes sense you need to consider that baking soda being a base
,a very mild one, and BP residue being slightly acidic, they would seem to cancel each other and be neutral. Care must be taken not to go to far towards the base because too much base will speed the oxidation process just like too much acid.
A good example is batteries. A lead acid car battery leakage will cause enough corrosion to ruin an inner fender. An alkaline D cell leakage will destroy a flash light. One is an acid the other is a base.
While it may neutralize the mild acid of BP I really think it is too much trouble for too little gain. IMHO
What causes rust is oxidation. Oxidation is in a sense just slow burning like rusting. A fast oxidation process is fire. Water is used to extinguish fire, it cools the burning material below the ignition point and smothers the material preventing oxygen in the gas state from completing the chemical chain reaction. Stopping this rapid oxidation or combustion.
Oil acts on the slow oxidation just like water does in the rapid oxidation. A good gun oil will coat the naked steel that will rust all by itself even in the
"neutral state". The oil will also soak into residual powder fouling preventing oxygen in the form of moisture completing the chemical chain reaction causing rust.
Oil and water don't mix. Water will always repel oil. That is why it is very important to make sure all moisture or water is out of the barrel. The naked spots where the water was will rust.
The bottom line is to make sure your barrel is dry before you oil it. It would be better to oil a fouled barrel well than not to oil a clean barrel at all.