Can this notebook be powered on without the bottom case attached?

A customer of mine dropped his Macbook on the corner of the notebook where the power adapter connects to the power jack. The damage to the corner has made it impossible to properly connect the power adapter to the jack, because 1. the case is warped and the adapter cannot quite reach the jack 2. the jack mounts on the bottom case were broken so the jack now sits loosely inside the case.

There appears to be no physical damage to the jack itself and I have tested that voltage is making it through the jack and through the motherboard to where the battery connects.

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 done to the computer.