If you want it to run without the board you have to unplug it from the socket on the MPU board. If you leave that plugged in then just unplug the connector from the reset board the machine will not boot.
As others have mentioned the board is to keep something from burning up should the MPU lock up. Not such a big deal in your home where someone is likely at the game while it is on, but for a machine on location if it locked up somone may not be there or not notice that a coil was locked on and could burn the coil and or transistor up.
If you have one without the reset board be sure you don't leave it unattended while on. I have 4 80a/b machines and the only one without the reset board hooked up is the one with a new aftermarket MPU board in it that doesn't have a socket on the board for the reset. That being said I have never noticed any of them locking up.