Yes, it always does, yet I cannot say how much - maybe negligible, depending on the graphics card and the state the graphics card was in as the guest has been shut down. Best would be to load the driver of the card after the VM has shut down and enable power savings.
If the card has a fan, it is not controllable without a driver and it runs, so it draws power. Fans draw a lot of power. If they're spinning fast, they can reach the same amount than other components. Last week we had a cooling outage in a customer data center and the power usage on a server doubled as all 6 fans ran at full speed. Never seen something like that.
What about not shutting down the VM and enable power savings inside of the guest for the card. Best would be to test you card, because every vendor can implement whatever they want in their cards. I read about the shine new ASUS ROG cards that work perfectly silent on Windows, but the fans cannot be controlled in Linux and they're roaring at full speed, always.