Yes you can X ray …but Image quality won`t be good. As you have said that it was a minor fracture- It may not even be seen when X rayed with plaster on. 3–4 weeks of Plaster - good enough for healing minor fractures. read more
You can have an X-ray with a plaster cast on, however the image won't be as clear as it could be without one. It creates more layers that the radiation needs to penetrate to create a clear image for the Radiologist to look at. Having a plaster cast on will create a cloudy and unreadable image. read more