No, and not because the effect is in any way small.

It is because a phone screen producing white light, looks white because it is actively generating white looking light. Compared to white paint, which looks white not because it generates its own light, but reflects other light, these are two different mechanisms for making things look ‘white’.

Your phone has a brightness setting, to keep ‘white’ the exact same shade of white despite whatever viewing condition you have. A white paint does not, and as a result, looks different depending on the amount of light in the room.

So in your hypothetical, a white phone screen won’t reflect less light as you presuppose - it’ll generate more heat internally - unless you cover the screen with white paint.