Greg,
Of course you can do this, but I'm trying to get away from AC cords, transformers, bridges, etc. What you describe will certainly work (I use such a setup for my mac mini DC supply -- smart charger, large AGM battery, and a regulator/filter that goes to the mini, the external hard drive and my turntable's motor) but it probably won't be as quiet as straight batteries, and of course batteries aren't silent or perfect either (that's why the final regulator/filter in my computer supply).
I've never tried NiMH for audio power, so I guess I'll find out what it's like.
As for me, the space I want to use this in is very starved for AC outlets, so a battery preamp is a good thing here. I've got 2 fast, smart NiMH chargers -- one that does two D cells at a time and the other that does up to 10 9v rectangular cells at a time, so for me it is just a matter of once every couple of months or whatever it turns out to be, taking all the batteries out at once, popping them all into their respective chargers, then putting them back in the preamp -- and I can keep the chargers elsewhere in the room.
With the quickie, it's so simple, so elegant, fairly flexible on power supplies, uses low voltage and doesn't get hot, so it opens a whole load of possibilities for creative expression that you simply can't do with the other kits. Once I verify that this dual mono setup and the battery sizing will work well for me, then I'll probably build some more of these as headphone amps -- especially for my neices and nephews when they get to an appropriate age. Got one coming up in January that will be 12, and assuming my sister is ok with it, she's going to get one nice birthday/christmas present from her aunt and uncle. Again, the low voltage and lack of heat play a big part in being able to do this. I just can't at this point see my sister allowing something like the s.e.x. or Crack in the neices' bedroom. And of course it will finally give me an excuse to make something in purple :-).
-- Jim