Icing a cake with meringue: can it be done in advance?
This is a pretty tricky question to answer without knowing what the climate is like in your area. 

Meringue is hygroscopic (absorbs water easily) due to the high concentration of sugars in the mixture. This means that any available source of water, including the air and the cake underneath, will donate water to the mix and make it soft fairly quickly and perhaps add a layer of liquified meringue between the cake and meringue if the cake is very moist. However, Italian meringue is fairly common as a topping on filled pies and is used as a base for buttercream icing, so it is quite stable as a mixture compared to some other types

If you can find some way to contain the cake in a sealed container, then it should last a reasonable time - overnight should be OK I think. I would make sure it is chilled if possible, for food safety purposes.

If you are somewhere where the air is dry, you will probably find that the meringue will hold fairly well outside a container for a few hours, however if the climate is humid, then the meringue will absorb moisture from the air quite rapidly and soften. How fast this happens depends on the relative humidity and airflow around the cake.