No, you can down shift without the clutch if you heel toe correctly and match the revs. The slight blip of the throttle counteracts the deceleration force to unload the dogs to allow it come out of gear. As you go through neutral, the throttle blip will speed up the gearbox internals to the same speed to allow them to engage without clunking, banging or simply not going in.
The way a dog box work vs a synchro is very different.
Power affects it slightly. More power means more force. More force means more output. More output means more speed.
For example, at one power level i got 10kph/1000rpm in 1st gear. After adding 100awkw and changing nothing else, i get just over 12kph/1000rpm in 1st gear now. So it isnt a huge factor in terms of how it affects your speed. tyre size and final drive would make more noticeable differences.