Your sub is doing one of two things. Either it is duplicating the low frequencies and passing the whole signal straight through, or it is serving as a lowpass filter. If it's the latter, which I suspect it is, then your sub probably has a crossover knob. Everything below the crossover point is being filtered out of the signal and sent only to the sub, in that case.
This is pretty easy to test for, luckily. Set the volume (not the crossover) on your sub to zero, and listen to the headphones. Then remove the subwoofer from the circuit (i.e. place a jumper on the back of your Nakamichi that goes from the pre out to the main in) and listen to your headphones again. If you notice a change in bass information, then your sub is also a lowpass filter.
You'll need a pair of RCA splitters in that case, to send a full signal to both the sub and the main in of your Nakamichi.
Regarding wattage and chargeup time, it's not terribly complex. Your transformer itself doesn't need too much chargeup time, just enough to build up a bias voltage, which relly only needs to be a few seconds. You can test this yourself, though. Play some very soft music into it with the headphones plugged in, and hear how it gradually gets louder. You can also charge it up right away by playing some reasonably loud music into it to start. Your headphones also require a bit of a bias charge, so when you charge up the energizer have the headphones plugged in (so don't go too loud). You shouldn't really need more than a few seconds of music at a decent volume.
Regarding wattage, you're free and clear. I've run my energizer off 1 watt SET amps, and off my NAD integrated putting out about 95 watts. Both sounded great. For an acid test, I'll plug it into my 300 watt per channel monster amps tonight and give it a listen. I suspect it will work wonderfully, though I'll not have much volume knob to work with.