Team cohesiveness does not necessarily lead to higher team productivity.

This statement is true - only because a team is cohesive doesn't mean that it is going to be very productive.
This doesn't only depend on the team itself, but also on the relationship between management and the working team. The team has the potential to be very productive, but it will depend on this relationship I mentioned. If it's good, they are likely to be productive, and vice versa.