That depends.
It may do wonders for efficiency, yet there are a number of ways it can breakdown: failing to complete regulatory or contractual requirements is a big one, since they rarely allow for flexibility. Clients may not receive the service they expect, so the organisation's reputation will be damaged. In cases like that, prioritisation only really works to diminish the possibility that too much time is spent on small tasks or that efficiency is reduced by doing things out of order.
It also turn small problems into a crisis. With staff already working at capacity, there are very few options for handling the problem.