no there is no need to circulate the air when the plants are sleeping. They are essentially asleep, not drinking, not using air, etc...(I believe, not positive).
In most grows you will find it necessary to run your exhaust and carbon filter 24/7 anyway in order to keep odor down. If I shut my exhaust fan and carbon filter off even for an hour my entire house stinks up.
Where are you running the dehumidifier? I run one but that is because I vent into a room in my house instead of outside.