If you're thinking of actually shoving the innards of a pedal into your guitar, I'd suggest using a battery. You actually could use an AC adapter and just put the AC connector from the pedal near the jack, but you'd be stuck with a second cord and a pretty short one at that. As an alternative, I think you can add some distortion to your signal with just passive components, basically what you want to do is clip the signal and add some filtering. As a final option, but that would take some designing, you could put a DI box in there as well and output your signal through an XLR connector. Those allow you to run a 48V DC 'phantom' power over them. You'd have to intercept the power in the DI box (it will probably be available at 9V because most DI boxes can also work on a 9V battery as well as on phantom power) and bring it to your disto circuit. The big disadvantage of this would be that you wouldn't be able to plug straight into an amp anymore, you'd have to run hrough a mixer that is able to provide the phantom power.