Actually I think you would be dead if your blood pH changed too much. Your body has ways of balancing itself to keep the blood pH balanced but allowing the body to constantly steal minerals from one's bones does not seem like a good way to keep the body alive for too long. If one can sweat out some of the acids by doing the baths then that can only benefit the person while at the same time build their alkaline reserves by doing the ML drink.
When you do the ML drinks the reaction between the lemon juice and the lime water turns into bicarbonate.