The recipes I am seeing don't age the cheese at all, but continue and cook/melt the cheese. In that case, I believe the baking soda is just for meltability.
I think it would have been a challenge to the Germans who came to Texas to continue their existing cheese traditions, without access to any temperatures to age cheese. I know my great grandmother dugout root cellars wherever she lived here in Texas, but that's still too warm for dairy/cheese. Guessing your grandmother's recipe is of the post refridgeration era.