first, how much current does your arduino need? the 5v within a controlelr is typically only able to supply a few dozen ma at most, and that includes powering it's own mcu, throttle, internal transistors/chips/etc., hall sensors, and so on.
so there's not usually much leftover after that.
you can, of course, change the 5v regulator out for one capble of higher currents, but htis will then need a higther current source so you then also have to hcange out the 12v (or whatever voltage) regulator that converts the battery voltage down for the 5v regulator input as well.
it'd be simpler to just get a small battery-voltage-to-5vdc dc-dc converter just to power your arduino. there's a lot of stuff that does that and it's usually really cheap.
so, if you only need a few ma to power the arduino, maximum, you can simply add a wire pair to the 5v and ground on your throttle, or hall sensors, or pas sensor, etc., without even opening the controller itself, and run those to your arduino.
but if it draws too much current it will drop the voltage on the 5v line too far, and the controller will operate unpredictably if at all. worst case it will damage the 5v regulator and cause the controller to no longer power on.