This is exactly correct. The caveat is that the rudder is trimmed for a particular angle of attack, so it will try to align based on how it’s trimmed, just like an elevator, even some ailerons. Some aircraft have rudder trim that is adjustable in flight, some only on the ground, and some not at all.
The “centered” trim/AoA occurs in a very narrow speed band (usually cruise), so it gets out of trim above or below that (and again, some can be adjusted in flight. It may not move much, but it may not exactly be dead-center and if you were to try to find the physical center of pedal travel, you might feel a little more pressure on one leg or the other.
But there isn’t a clicky center-stop like found on most gaming systems. I actually put a couple Velcro strips under the rollers inside my pedals so they don’t automatically self-center. This isn’t exactly realistic, either, but it keeps me on my toes, pun intended.
Anyway, the centering mechanisms of our yokes, sticks, gamepads, pedals, etc, do us some disservice to that effect. Other than spatial proprioception and disorientation, control pressure/feedback is the biggest realism hurdle in the sim.