This will not work. This is a sensing circuit only. The controller most likely has pull-up resistors on each pin that only allow micro-amps to pass through the resistor to pull the pin high. When you connect a switch to the break out box, the switch connects the pin to ground. The controller senses the low state and acts upon it.
I tinker with microcontrollers all the time. I do not know the specifics of what is inside the Apex. But, most uCs use about a 47kOhm pull-up resistor. If we assume it is 5V (TTL) logic, then the pull-up resistor passes 106uA. That is not enough to power an LED indicator and would mess with the I/O pin state anyways (since most LEDs have a 2V or more forward voltage.) Most newer uCs use 3.3V logic and, if that is used here, the same 47kOhm resistor only passes 70uA. Most LEDs require about 20mA. I've seen LEDs that use single digit mA but those are rare, and dim. I've never seen an LED that pulls less than 1mA.
Good luck, let us know what you find.