I should think it would work, though it would give you a permanently attached cord. You would probably want to rig up some sort of strain relief to prevent the cord from being pulled from the connection and possibly damaging the system. Also, be careful when soldering to avoid heat damage to nearby components. A possibility to consider would be to wire a socket to the motherboard which would hang outside the case and still give you the option to go cordless.

Might be possible.