Properly managed, a team with members in multiple time zones can be enormously productive if the work is such that it can be handled in shifts. Software can actually be done this way. You have to be culturally willing to do it.
It's horrible for the people who have to work in such a system. We have people in India and during phases where you have to collaborate a lot, either the US people or the India people have to constantly work at night. And the company demands this in addition to regular working hours. We also have people in South america and that's much better to deal with because working hours overlap during the day.