Yes, he did. His unit got trapped by Germans at a small French town known as l'Epinette. He rescued his unit from the Germans using his bow and two machine guns he carried around with him. It seems unbelievable but, Jack Churchill was the epitome of craziness. In addition to a bow he was famous for his broadsword and can be seen in a picture charging onto a beach with just his sword (this one found on http://upload.wikimedia.org/wikipedia/commons/d/d2/Jack_Churchill_leading_training_charge_with_sword.jpg) . He captured 41 Germans using his broadsword. He also enjoyed playing the bagpipes. During a commando raid in Norway Churchill jumped off the landing craft and began to play his bagpipes before charging the Germans.

The book "Commando" by Peter Young has a lot of information on this topic.

Follow-up question: Would this be the last recorded incident of someone being killed by a bow in battle?