No, there will be one excuse after another. Starship isn't human rated and only Orion is rated for human deep space flight. So something else will still be needed to launch Orion to that lunar trajectory. That something else is SLS.

Now the obvious solution is to rate Dragon for deep space and launch humans in that on a falcon and have it meet up with a starship in LEO. But getting that will probably take more years and billions paid to to the Orion and SLS POR before it will actually come to pass.

Never underestimate the power of a self-licking ice cream cone.