When you look at the ultrasound, fraternal twins have separate placentas while identical twins share a placenta. This is already visible at 7 weeks of pregnancy. The difference is very important to care during the pregnancy as identical twins have more risky pregnancies due to more possible complications so I would be very surprised if the obgyn does not notice this.
After more research into twins I found I was wrong. Actually, it is more complicated than I thought and placentas are not so straightforward, so the anonymous poster can be right.