Yes I have had placenta previa at delivery 2 times. It is normal for the placenta to be in a low position early on in the pregnancy. If the placenta has moved up with the uterine development after 20 weeks and is not covering the birth canal opening at all, then the mother is ok to have a normal delivery as far as that is concerned.
If it hasn't moved, close monitoring of the position of the placenta has to be taken as the pregnancy progresses. The mother may be put as a high risk pregnancy case until it moves. The doctor may counsel for no sex, less standing, or even complete bedrest as he sees fit.
If there is placenta previa at birth or even partial placenta previa, then the mother must deliver by c-section.