The following might do what you're looking for.
In your layout, place a layer above all your other layers.
Add the "Adjust HSL Mask" effect to this layer. (You can click the layer in the layer panel and edit it's properties in the properties panel.)
Set the layer's "Transparent" property to "No".
You should now be able to post-process the entire game with the "Adjust HSL Mask" effect.
To smoothly fade in an fade out the effect, create two number variables.
We'll use these to control the effect's saturation parameter.
In this example, I'll use functions as the triggers for starting and stopping the desaturation effect, but you could use anything you want.
* On function "desatOn": Set "targetSatValue" to 100.
* On function "desatOff": Set "targetSatValue" to 0.
* Every tick, if followSatValue < targetSatValue: Add 1 to "followSatValue".
* Every tick, if followSatValue > targetSatValue: Subtract 1 from "followSatValue".
* Every tick: Set "Adjust HSL Mask" param 1 (the saturation) to "followSatValue".
(Actions in italics.)
When the function "desatOn" is called, the targetSatValue is set to 100, and the followSatValue will begin gradually counting up to the target. When the targetSatValue is set to 0, then followSatValue will count back down to the new target value.
Hope that helps.