One would think so but paradoxically the opposite is the case.

If the Sun was to switch off, the enourmous heat store of the tropical oceans would be released in a very volatile manner because of greatly reduced vapor pressure at the ocean's surface. The oceans would boil. Once the oceans cooled off, which could take weeks or months, then yes, atmospheric overturning would slow down and eventually we would have a dry and fairly windless planet. The Sun could turn back on but it would still be cold and dry because of the overall change in Earth's albido due to the huge advance of the ice sheets in the northern hemisphere.

Have you ever taken a big pot of hot water outside into air that is -10C? I think you would be suprised to see what happens.

"Evaporation from open water surfaces, like the ocean or lakes, can be simply estimated as proportional to the difference between the saturation vapor pressure at the water surface and the actual vapor pressure above the surface, although the higher the wind speed and the greater the turbulent mixing of the atmosphere, the greater the evaporation."

Turbulent mixing of the atmosphere are the key words.

[link to www.arl.noaa.gov]