Is it normal for boys to feel the urge to dress completely as a girl?

Yes. Crossdressing is a normal phenomenon. It is simply still taboo in many cultures. Other societies and subcultures are more accepting however. One must differentiate however whether the person FEELS as though they are a girl or if they simply prefer to dress as a girl. If it is the former, this is more indicative of transgender/genderqueer feelings. If it is the latter, then the individual is most likely a crossdresser, and many crossdressers feel the urge to dress as a different gender altogether - some want to do this most of the time, while others prefer to do it only occasionally.