That’s a new one on me. Guess anything is possible. I’ve installed dozens of stereos over the years and never came across one like you describe. Usually the memory (yellow) wire is for the presets/clock to be remembered in case of a power loss to the main power to the radio not to supply power for the radio to play. But if the OP isn’t sure about using his radio he can do the same with a cockpit light or similar 12 volt item.