"I know the higher the emissivity a surface has the greater its ability to absorb heat (IR), however, is a painted surface able to reject or shed heat better? An example would be does a painted engine run cooler than a unpainted metal engine or hotter or the same temp?"
If an object has a higher temperature than its environment, then increasing its emissivity will certainly lower its temperature. As an example, lets look at the motor in the illustration. It has a cover made of stainless steel and is very shiny. Let's assume its emissivity is 0.1. We have measured its steady state temperature at 150 F. The rate of heat generation of the motor has to be exactly balanced by the rate of heat loss from the motor. So, in this case for simplification, we will only consider convection and radiation. The numbers are shown in the illustration.
Now, if we painted the motor with flat white paint, the heat transfer will change. We still have to get rid of the 66 Btu/hr being generated by the motor, but if we assume a new emissivity of 0.9, then the huge increase in the radiation loss will reduce the surface temperature to 118 F as shown.