Would the Earth function the same spinning the other way?
That would have many consequences. For example the Coriolis force would change the sign. Thus wind around pressure systems would switch the direction from north and south hemisphere, but also the Ekman spiral in the ocean would be affected. Surface heating at sloped terrain will different, as the sun would rise in the West. This would change thermal induced circulations. And the conservation of angular momentum is important for the general circulation.

I would expect major impacts on the resulting climate, even in an equilibrium mode, which does not account for the acceleration to the oppose rotation velocity.

During the time of stopped rotation additional circulation systems can be expected, which exchange energy between the day and the night side of the earth.