Yes. That makes a great deal of sense.
Those aerodynamic forces do still "precess a gyro" though, right?
There's still a lot of angular momentum to redirect.
The torque from the changed lift on the blades acts about 90 degrees out of phase from the input, perpendicular to the intended direction of motion, to shift the angular momentum of the disk in the direction intended, pulling the hanging part along as desired, with a response speed that is still limited by the size of the torque that can act. I guess the lift and angular momentum both scale with disk area and with rotation speed squared, so it naturally coordinates.
It's very impressive to think how the pioneers got it all to work.