User 2012-11-19 20:11:21 Can i use a Adapter 12V 2A for this product?Will it burn my arduino board? Admin Reply : Nop, Arduino main board does not take power from this shield. If you supply 12V to this motor shield for motor supply it is within voltage range 7V to 12V. If you supply the adapter to Arduino main board, it is still within range, 7V to 15V.
It depends on how much your motor draw. Arduino main board should have some kind of diode to protect the polarity, diode will have maximum current rating too. I don think the Arduino main board will damage, just that diode will be super hot if the current drawn by motor shield is at 2A. BTW, the adapter is also at max 2A, not really recommend taking 2A from the adapter.