The receiver is fully connected to the Ardupilot with a spare channel to play with.
I've not used these bits, what exactly is the has a spare RC channel got to do with the Arduino hanging off the Ardupilot?
If it's just an RC channel I don't see how it's of any use for "talking" to the Arduino except in the most simple of ways. Certainly not for reprogramming. That said
I would like to somehow change how the LEDs are behaving
You don't have to "reprogram" the Arduino to do this, just write a program that accepts some data from the Ardupilot and drives the LEDs differently according to the data.
That should be possible using an RC channel. Do I have this right?
RC channel ---> Ardupilot ----> Arduino
If so what do you get into the Arduino? Pulse train, SPI data, something else?