There is no legal obligation to involve employees: employee-ownership companies can, within the framework of most corporate and ERISA law, ignore or even actively resist employee desires for involvement.
Nonetheless, it has become conventional wisdom in management literature that involving employees in making decisions can make a company more customer-focused, more cost-conscious, and quicker to adapt to changing market conditions, in addition to increasing job satisfaction and employee retention.
In the context of employee-ownership companies, the case for employee involvement is even stronger. The advantages of employee involvement are magnified for employee-ownership companies -- involvement taps into the unique power of employees' expectations about ownership.
Psychologists Rudmin and Berry researched the roots of psychological ownership and found three main causes, one of which is a degree of influence over that which is owned. (Understanding the means by which the object became owned, and information about the object are the other two.)  Unless the company engages notions of employee involvement, people are unlikely to think and act like owners.
Employee-ownership companies that succeed in building psychological ownership through employee involvement tend to see a substantial payoff in dollar terms. In his study of ESOP companies in the state of Washington, Peter Kardas wrote that "the combination of employee ownership and significant participation makes it possible for employee ownership companies, on the average, to have an advantage unavailable to their competitors." 
For more research on the performance effects of participative employee ownership, see
 Rudmin, F.W. and J.W. Berry. 1987. "Semantics of Ownership: A Free-Recall Study of Property," The Psychological Record, Vol. 37, p. 257.
 Kardas, Peter. 1997. Comparing Growth Rates in Employee Ownership Companies to their Participatory Competitors, Washington State Department of Community Development, Olympia, WA, February, p. i.