so I finally got one of these and learned what the connections are. after giving the board power and seeing no voltage between com and nc/no when button is pressed. You have to provide power to com, power doesn't go through the board. So All he's doing by shorting here is sending the power from the power supply to the common for the relay.
Yes you can you hook NC & Com and and +12V/com from wireless receiver up to the door access control's panel to the Push terminal and com, to +12V and com