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If you want to know for sure, put an amp meter or a kill-a-watt meter on the fan and see how much more energy it uses, if any, when you close off the vents.
Guessing will get you no where.
A remote sensing thermometer might also be worth while, I have one that tells me humidity as well for both the indoor and out door sensors, knowing if a closed off room is damp or below freezing could save you a lot of money in repairs.
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