Short answer (From www.smartphonesource.com):
Two things I would check: Flip Closed-->Menu-->Settigns-->Sounds-->Vocie Answer
This defines if you get the voice prompts when in speaker phone mode or connected to a handsfree car kit.
Flip Closed-->Menu-->Settigns-->Accessories-->Headset Ringing
If enabled to ring through the headset, you will be voice prompted, provided the first setting above is enabled.
So based on this, here are the scenarios that will provide voice answer:
1) Voice answer enabled and connected to a handsfree car kit
2) Voice answer enabled, headset ringing set to ring through headset, headset plugged in.
3) Voice answer enabled, speaker phone enabled.
External power has no impact on this functionality.
Hope this helps...
Regards.
Dave