Not necessarily.
It depends on the enclosure size, the humidity of the room it's in etc. If you want to be sure, go and buy yourself one of the digital combo thermometer/hydrometers which have the two wires and two sensors, they cost between R100 and R200 depending on where you buy, and place the humidity sensor inside your tank and see what the humidity is with only a water dish.
If the humidity is low, then you can also moisten your peat. But if it's high, then you don't have to make the substrate damp at all.
The arboreal tank I built especially for Avic. versicolor was tested with nothing inside but water in the reservoir and the humidity was 90%. So I leave the peat bone dry.
HS