Putting the LED behind the switch is not going to dump enough current to tell the LC1 to calibrate.
I'll have to look at the boat but if I remember right the light plays a role in letting you know the wideband is heating up.

Just make sure their connected at the same point on the calibration wire and the same point for ground.. they share.
I'll explain how it works in what I understand. Electricity is similar to water as it'll take the path of least restriction.. but to ground. That LED is only going to use up XYZ amount of current.. I think its like 10-50mA depending on the color, which is not a lot of current. That switch is going to be able to dump the rest of the current to ground.
Unless by some act of shear amazingness of wiring you get the ground from the button switch shorter than the length of the wire to the LED, the LED will consume the current first which is how they show you the blinking light as you hold the calibration button down.
Now I am no electrical engineer.. and that is how I see it.