Before playing in the NHL, Gélineau served in the Second World War and was awarded the British Empire Medal for actions in 1944.
He also played intermediate basketball, football and varsity baseball which resulted in a tryout with the Boston Red Sox.
The last McGill goalie named team captain, Gélineau backstopped the Redmen to the 1946 Queen's Cup championship.
That spring, he was called up to the Boston Bruins in the National Hockey League, becoming the first goalie in 30 years to play in the NHL while still attending university (two decades later, Ken Dryden duplicated this feat while studying law at McGill and playing for the Montreal Canadiens).
He won the Calder Memorial Trophy as the NHL's top rookie in 1949–50 but was unable to capitalize on his early potential.