It really depends on how you'll use it. Mostly it runs on it's internal battery (6-12. hours) but if using it with a source component, the power will come from that component as follows:
If you turn the iDSD on before making the connection to the source component, the iDSD will run on. it's battery until it needs a charge, and then the source device will supply power. I'm not sure if the battery will charge and then revert to battery-only,, but that's probably in the manual.
The best way I kknow of to improve the power to the iDSD is with an iDefender with an ipoweer (or similar) power supply, but that is only my guess. It really depends on the source component's power supply. You can skip the battery altogether and go from a power supply directly into the iDSD, in which case, yes, a better linear supply will most likely give some sort of improvement -- but at least with the Black Label, the noise filtering circuit is built into the DAC/amp itself.
I love my iDSD Black Label and will never part with it.
BTW, battery life depends mootly on power level setting and difficulty of driving the cans in question. I use mine mostly with IEMs, so always use the Eco mode, but crank it up for the Oppo PM3s, though they are very easy to drive. Sorry, but I never really timed the battery life for myself.
If you're using the usb port for power, then you should get some more mileage out of a better supply than a standard-issue apple supply, but how much, I don't know. -- but you are then probably going to have to use spdif for the input, so no native DSD.
Sorry if this confused you any further, but it really depends on how you plan to use the device.