Should whole house humidifier leak cold air in the summer?
Leaking duct work regularly costs users 10% when leaking into non conditioned air spaces but if the leak is totally enclosed within the living space envelope it really is not helping much.
Every air leak in an attic for example is saving $ if the leak is in the air handler closet it may save some but is not as effective as the attic.
As for humidifiers I like them to be easy access ultrasonic ones to verify they are working and Venturi ones to verify they have not plugged or are dribbling so for that reason I do not go crazy when sealing these up as I check mine several times a year.