Yes. An E-2 spouse is employment-authorized incident to status and may work for the enterprise or anyone else, without a separate employment authorization document. Children may study only.
The spouse's work in the business is permitted; count it in the plan honestly
USCIS treats the spouse of a Torbay E-2 investor as work-authorized by virtue of the dependant status itself; the spouse's arrival record, marked to show the E-2 spouse category, is what a bank or payroll provider will ask to see. Running the office, dispatching technicians or taking an unrelated job are all open to the spouse. One caution: if the spouse's unpaid work is what makes the company viable, the officer may see an enterprise that supports only the investor's household, which goes to marginality. The plan should show hired staff beyond the couple, and if the spouse is to be paid by the company, show that too. Sons and daughters under 21 can be enrolled in school on the dependant status but cannot be employed, and the status lapses on the 21st birthday; since E-2 offers no route of its own to a green card, a teenager near that age needs a separate plan. If the principal's E-2 lapses or the company stops qualifying, every dependant's status lapses with it.
Hypothetical example: the spouse of a Torbay custom-cabinetry investor plans to keep the books without pay while the business delays its first hire. The family may do that work only if the enterprise otherwise meets the E-2 requirements, but the plan must not conceal a marginal operation dependent solely on the couple. A first review compares projected payroll, signed customer work and working capital with the household's role. It should show capital already committed and at risk, not merely a hope that family labour will make the company viable.