Probably not. This is probably the same kind of motion sickness that people get from VR headsets. This ride is not a crazy mouse; the spinning hardly seems extreme. If your eyes are telling you one thing though, and the your body is telling you another, that can affect people in all kinds of weird ways, and some people are just way more sensitive to differences between those two stimuli.
If the screens are tracking the rotation of the cars, then they would need to both significantly tighten the timing between the two, and shoot for really high refresh rates on those screens. That's a technology jump that is more than a few years away still.