Is there any way to predict/calculate the pH level of a recipe when the level of individual ingredients is known?
Short answer — it's definitely not that simple.  For one thing, the pH scale is logarithmic, not linear.  For another, almost every acid and base you're likely to encounter in a kitchen is “weak” - meaning there's an equilibrium between neutral and ionized forms. When diluted, the equilibria shift. When the temperature changes, the equilibria shift.  When mixed, the equilibria interact with each other.  

If you're working for a big industry and filling railroad cars with your recipes, and doing the same reactions again and again, and trying to maximize profits, it could be worth doing the math. But for a small scale cook - you could probably get as far as accurately predicting the pH of a mixed drink, but not a lot further, I think.