Can we have a policy forbidding employees from saying disparaging things about the company on social media?

Not in such broad terms. Under the National Labor Relations Act (NLRA), employees have the right to discuss terms and conditions of employment for mutual aid and protection. That includes the right to discuss wages and working conditions, and to do so on social media, if the employee prefers. The National Labor Relations Board has ruled that forbidding disparaging remarks on social media may discourage employees from exercising their NLRA rights, and is therefore not allowed. However, the Board has accepted policies which give specific examples of prohibited conduct (such as harassment, threats, etc.) and found that employees should not misconstrue the policy to prohibit the exercise of NLRA rights.