If I am correct, the case of the .22 Win Auto is the same rim and diameter of the .22 WRF or Mag.
If you were correct it might be. However, you are not correct. Check Cartridges Of The World
and you will see that the rim is .310" and body diameter is .250", substantially larger than the .290" and .240" for 22 WRF/22WMR.