The wall would not succeed at it’s intended purpose. Hadrian’s Wall and the Great Wall of China didn’t work for their intended purpose either.
Empires who set their borders and hide behind them and start encouraging the successful parts of their population to have low birth rates inevitably fail
You are correct about low birth rates, but why would that result from building a wall? I'm inclined to think that making it more economically practical for solid citizens to have children would have a positive effect on the birthrate of that part of the populace.