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For my 2006 Macbook Pro's with intel core 2 duo... you don't need the power cable plugged in.
For my 2011 Macbook Pro with Quad cores... seems like you need the power plugged in no matter how charged your battery is. Not sure why this changed.

2006 Macbook Pro is running OSX 10.4.11
2011 Macbook Pro is running OSX 10.6.6
 
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