Does top spin and bottom spin affect the cue ball's path after hitting a cushion?

From what I've gathered from all the replies, the cue ball will curve after hitting the object ball and then curve after hitting a rail as well until it's rolling smoothly on the cloth.

So my idea of angle in = angle out in my first diagram is incorrect if the cue ball still has a lot of top spin when it hits the rail (not rolling smoothly)? Maybe I just can't tell but when I play shots like the one in my diagram it doesn't seem like the cue ball curves off the rail and it only curves after hitting the object ball. Is it possible for the curve off the rail to be so slight that it's hard to notice?

This is opposed as to when I kick the cue ball into a rail with spin and notice immediately that the cue ball curves

Does top spin and bottom spin affect the cue ball's path after hitting a cushion?

Given your expertise I always must defer to you in situations such as this. So that means I'm wrong when I say the CB only curves once.
In general the cue ball will have some curve immediately after it hits any object. If you play a 3-cushion shot with follow off a ball, the cue ball will curve after it hits the object ball, and then it will curve after hitting each cushion. I think "the CB curves only once" is correct only if you have a lot of other explanation.

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