At the outset it is important to clarify that the term "management science" used in the question refers to particular set of management methods which are also given other names such as OR (operations research) and quantitative techniques. These are all methods or techniques of decision making and control make use of some form of formal model or representations that facilitate analysis and understanding of various factors affecting decisions. These methods often also enable identification of optimal decisions. Some examples of management science techniques are linear programming, economic order quantity (EOQ) formula, queueing theory, simulation, PERT and CPM, and Statistical Quality Control (SQC).
It is quite true that many methods of management science make heavy use of statistics. We can also say that if we remove form management science all the techniques using statistics than the balance will constitute a small part of management science. However, it is not correct to say that without statistics management science will bear no fruits or will have no roots.
Some of the earliest management science applications such as linear programming or, which are also some of the most widely used and most useful, make no use of statistics.
Statistics is useful only when dealing with subjects and situations involving some degree of measurable uncertainty. In a real life world, particularly where decision and actions of a large number of people are involved statistics is a great help. And many of the management decisions and actions deal with people. Similarly when we deal with random variations not within control of managers, such as variation in dimensions of a component manufactured on a mass production machine with a give set up, or the time of a machine breakdown, or the weather condition, statistics is a valuable help. But still statistics not essential for all management science methods. It is just one of the many scientific discipline that management science uses.