After you get the nut torqued to the shaft, I assume new engines still have an overrun clutch in F gear which allows the engine to drop in rpm while the prop is still turning at whatever speed the water running past it causes as you decelerate. To check this, with the engine off, and the shifter in F gear, turn the prop cw (looking from the rear) and watch it and the propshaft move out (from the lower unit housing) slightly then jump back (under spring pressure). This is indicative of the overrun clutch riding over the "sawtooth" gear arrangement. This should not be confused with independent movement of the prop to the shaft. Here the prop and shaft are locked together and both move in unison. The clutch affects the prop shaft internally so if you have the prop locked to the shaft, both will move in unison. Distance here is more like 1.4". If you turn/attempt to turn the prop ccw, it will offer significant resistance and the crankshaft will have to turn brfore the prop will turn.
If still in doubt, go to a Mercury dealer and do the test on a new engine in the show room. Won't take but a minute.