No. A child in E-2 dependant status may study but is not employment-authorized, even in the family business. Only the E-2 spouse is employment-authorized incident to status. Dependant eligibility ends at 21.
Children study; the spouse works
Hypothetical example: the couple's daughter expects to help at the centre after school for pocket money. In E-2 dependant status she may attend school but may not work, and informal help in the family business is still work. Her mother, as the principal, and her father, as the E-2 spouse employment-authorized incident to status, may both work at the centre.
When the daughter turns 21 she will no longer qualify as a dependant, so plan for that date within the renewal cycle; her own studies or a route of her own would decide what she does next. Confirm every family member's citizenship: as dependants their nationality need not match Canada's treaty status, but a member who holds only Canadian permanent residence may need a visa stamp from a consulate. E-2 offers no direct path to permanent residence for any of them.
Family review should identify each dependent's citizenship, passport validity, relationship document, intended travel date, and independent plans for study or work. Those records do not substitute for the investor's qualification, but they shape the filing sequence. Hypothetical example: a dental-laboratory owner expects a spouse and a twenty-year-old stepchild to join later.
The reviewer obtains the marriage record, custody-related documents where relevant, and evidence linking name changes before the business filing is finalized. Waiting until departure can leave little time to correct a civil record discrepancy.