I didn't think they had radar in 1937. I thought it was invented during the war, and was a huge aid to the British during the Battle of Britain, and then rapidly advanced to aid AA firing by the allies. In Churchill's massive and detailed seven volume memoirs about WWII, there is a portion titled "War of the Wizards" which deals with the rapid advance in technology during the war and its effects.
Radar was under development, especially in the UK in 37 and had been used very experimentally in directing naval gunfire. But the idea that a USCGC in the South Pacific would have a working radar set is absolutely a fantasy.