The current "Cure" for this bacteria does involve reducing the body temperature below normal body temperature to kill the bacteria, Yes it is feasible, but there are more practical ways than causing a coma such as sealing someone in Ice water for 10 minutes and reviving them, in a span of 3-4 months you would make a recovery.
"The first, a 12-year-old girl, was diagnosed with PAM approximately 30 hours after becoming ill and was started on the recommended treatment within 36 hours. She also received the investigational drug miltefosine 7-9 and her brain swelling was aggressively managed with treatments that included cooling the body below normal body temperature (therapeutic hypothermia). This patient made a full neurologic recovery and returned to school. Her recovery has been attributed to early diagnosis and treatment and novel therapeutics including miltefosine and hypothermia" (CDC website)
"The remarkable case of Anna Bågenholm shows how dangerous—and protective—extreme cold can be. In 1999, the 29-year-old Swedish radiologist was skiing in Norway when she fell into a frozen stream, becoming trapped headfirst under a 7-inch layer of ice. After 40 minutes, she suffered circulatory arrest; she wasn’t pulled out until over an hour after falling in. Yet the severe cold had cooled down her brain and body to a core temperature of 56.7 degrees, and after being rescued and revived, she woke up without any brain damage and recovered completely after a few months" (from the second site)
I base my findings on these two websites
How to survive cardiac arrest