Yes, you are correct. If the curvature was extreme, the ship would experience tidal forces, but not proper acceleration as a whole."Consider a spaceship passing a planet: The spaceship will experience 'gravitational attraction', meaning the effects of spacetime curvature, departing from a constant velocity, and experience a proper acceleration in doing so."
Isn't that incorrect? Assuming the spaceship is drifting past the planet, the ship would always be in inertial free fall right? No proper acceleration, no reading on the accelerometer?