The Mosquito most certainly utilzied wood in its construction, as did many of the aircraft designed and built in Britain. Wood, like plastic, does not reflect radar waves nearly as well as metal.
However, its powerplants, propellors, armament, and various other components were most certainly made of metals. While its radar cross section might have been lower than an all-metal aircraft, it is likely that the difference would have made the detection range a modest amount lower. Otherwise, all allied bombers would have been made of wood and flown at night untouched by the the Luftwaffe.
