It depends on the polarization of the incident beam: (circular on linear polarization) and the relative angles between the consecutive plates. So considering the configurations that make sense to me:
1. linearly polarized incident ligth
*after 1/4 wave plate which principal axis is 45 degrees relatively to the incident polarization, you obtain circularly polarized ligth.
*after the 1/2 wave plate you still have circularly polarized but of the other sign, whatever the relative angle between the axis of the first 1/4 wave plate and this 1/2 wave plate.
*The next 1/4 wave plate transforms the circularly polarized ligth into linearly polarized with a direction depending of the direction of the last 1/4 wave plate axis.
Rotating th 1/2 wave plate will have any consequence. This setup is weird because you can obtain the same effect (rotation of the initial linear polarization using only one 1/2 wave plate...
2. The incident ligth is circularly polarized:
*after 1/4 wave plate you have linearly polarized ligth 45 degrees with respect to the principal axis of the 1/4 wave plate
* The 1/2 wve plate rotates the polarization of twice the angle between the axis of the 1/2 and 1/4 wave plate.
*The additional 1/4 wave plate will transform the linear polarization into circular polarization if its axis is oriented 45 degree with respect to the linear polarization.
From that configuration, rotating the 1/2 wave plate by 45 degrees wil change the sign of the final circular polarization.
Usually the incedent beam is linearly polarized incident ligth. Just as Remi and Jean said, there will be two kinds of results in your question, which all depend on the angle between the crystal's axis and polarized direction of the incident beam.
1. After the first 1/4 plate, if the angle is 45 degree, the 1/2 plate will be useless. Because the incident polarized light has been changed into circular polarized light.
After the last 1/4 plate, you will get the linearly polarized incident light. Because any directions' changes are equal to each other.
2. After the first 1/4 plate, if the angle is not 45 degree, the incident polarized light will be changed into elliptical polarized light.
The 1/2 plate will change the polarized directions of both the long and short axis of the elliptical polarized light. The angle change depends on the the angle between the crystal's axis and polarized direction of the elliptical polarized light. If it is A degree, the polarized direction of the elliptical polarized light will rotate 2A degree.
After the last 1/4 plate, you can get a linearly polarized light or an elliptical polarized light. which depends on the angle.