Changing Protein Content of Flour
Sodium bicarbonate on its own is not baking powder but baking soda. A mixture of such with all purpose flour will not change the content of gluten-producing proteins beyond very slightly lowering their content per equal (to AP flour) weight of mixture.

The way the gluten forms in a dough/batter, and the way the whole product will brown/caramelize while baking, will actually be somewhat altered due to alkalinity, but this would still not mean equivalent behaviour to cake flour. Also, potential extra leavener (if an acid is present) will be there in addition to what the recipe describes.

What such a mixture, if using actual baking powder instead of baking soda, could be intended to substitute for would be self raising flour.