Can a simple infection cause gamma globulin levels to decrease below normal range? (0.37 when normal is 0.7-1.6)?

No: Very unlikely, unless the patient is already immune compromised, main causes for this low level would be diseases/disorders leading to loss of protein from gut/kidneys or malnutrition. Low level of immunoglobulins has other causes though, lymphocytes problems, either T cells or B lymphocytes, that lead to immunodeficiency states, wish you wellness