This depends entirely on the school, the department, and your classmates. If there is a pro to the American system is that it offers a substantial amount of flexibility. In my PhD program in biochemistry there was someone that studied Greek classics for an undergraduate degree and someone who spent seven years as a bartender before going back to study for his PhD.
Both of those people are nontraditional students and have done really well, both publishing a lot as well as getting teaching/post docs at nice institutions.
Such a move would be impossible in say, the French or nordic systems.