How is TAS affected by wind? Does True Air Speed (TAS) change with wind speed and direction?

My understanding is that if an aircraft were travelling at 470kt TAS, with a hundred knot tailwind, the ground speed would be 570kt. In this case the TAS would remain the same, regardless of the wind, but the ground speed would change.
Correct.  True airspeed refers to the actual speed which the aircraft is moving through the air.  Ground speed is the speed at which the aircraft moves over the ground.  The formula

$v_\text{ground} = v_\text{true} - v_\text{wind} \cdot \cos(\alpha)$

Where  


$v_\text{true}$ is the true airspeed
$v_\text{ground}$ is the groundspeed
$v_\text{wind}$ is the magnitude of the winds aloft  
$\alpha$ is the angle of the winds aloft relative to the longitudinal axis of the aircraft.