On some machines the method used to detect that the cash box is not installed can be bypassed so that an error will not occur. For example, if there is a security switch near the cash box that gets activated when the cash box is removed then you can disconnect the wires from the security switch and connect them together, making the machine think the cash box is still in place. The method of detecting the cash box varies from machine to machine, someone familiar with your particular machine model could say if bypassing the cash box detection is possible.
I'm pretty sure in the casino when they come around and empty the cash box on the slot machines they don't turn them off. They just open the door, remove the box, insert another empty box and close the door - all with power on the machine. So it won't hurt the machine if you try powering it up without a cash box installed.