Charging the Macbook battery without the bottom case attached.

I have Macbook 13" white (late 2009), the one with the rubber bottom. A customer of mine dropped the notebook and damaged the corner of the top/bottom case where the power adapter connects to the power jack. Now the case is bent slightly too much for the adapter to properly reach and seat against the power jack.

That brings me to my question. I have noticed that the motherboard has sensors all over it and I am guessing that the motherboard will not allow the computer to power on unless the bottom case is properly seated against it. I am wondering though, if the bottom case is off (so that the power adapter can connect to the power jack) will I be able to charge the battery to turn the computer on? This will allow me to rule out if any other damage has been made to the computer.