No. Dependants need the appropriate process for their circumstances. USCIS describes Form I-539 for eligible family members already in the United States seeking E-2 dependent change or extension, while those abroad have different steps.
Confirm authorization before spouse employment
A spouse in valid E-2 or E-2S status generally has work authorization incident to status; a pending request alone should not be treated as that status. Unmarried children under 21 may seek dependent status without work authorization. Review each person’s approval or admission record and acceptable employment evidence rather than assuming the principal’s paperwork covers everyone.
Assuming the household travels with the principal is the failure that costs families most. A dependant’s status has to be requested or applied for on its own facts, and an approval for the investor does nothing automatic for anyone else. Spouse employment depends on holding valid E-2 or E-2S status and being able to evidence it; a pending request is not that status, and an employer who accepts it may have to unwind the hire.
Hypothetical example: a corporate training provider’s founder relocates in September on the basis that the children can enrol and the spouse can join the U.S. team after the winter break, and both assumptions turn out to rest on filings nobody had made. Map each person’s route before the school year is chosen.