The answer is yes; prolonged vigorous crying can result in alkalosis in an infant. Same mechanism as hyperventilation, or vent settings that are too high. A crying baby and an alcoholic as the lone survivors of a biological "invasion" because they did not have normal pH levels was the central premise in the book, The Andromeda Strain, Michael Crichton's first novel in 1969. It was recently re-released.
"Alkalosis is caused by hyperventilation that accompanies hysteria, anxiety, or prolonged crying. " http://ull.chemistry.uakron.edu/genobc/summaries/chapter25.html
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