Only with employment authorization of their own. A qualifying E spouse — a legally married spouse in that status — is generally authorized to work incident to valid status, evidenced by the E-2S notation, the I-94 record or other applicable proof. Being married to the owner, living in the United States, or being paid by the company does not create that authorization.
Plan the back office before relying on it
If dispatch depends on one person, decide what happens while their own application is pending, since each family member has a separate process and no shared date is guaranteed. Unmarried children under 21 may accompany as dependents, but dependent status gives them no work authorization. Consider a hired dispatcher or a contracted answering service as a bridge, and record that cost in the staffing plan.
The evidential point here is that a spouse's permission to work is proved by that spouse's own record, not by the marriage and not by the company's payroll. Keep the spouse-specific evidence with the household documents rather than in the corporate file, since it will be asked for in ordinary employment contexts. The planning failure is building the operation around unpaid family labour that has not yet been authorized: a dispatch function staffed by one person whose own process is still outstanding is a single point of failure for the whole enterprise.
Price the alternative before you need it, so that a contracted answering service or a hired dispatcher is a decision already costed rather than an emergency.