No. The spouse’s own status and appropriate evidence govern their work permission.
Keep the dependent record separate
Qualifying L spouses may work incident to appropriate status with required documentation. The principal’s payroll or project history is not a substitute for that evidence.
Children admitted in L-2 dependent status may enrol in school and appear among the nonimmigrant classes permitted to study, so schooling is straightforward. Record the spouse’s classification, admission record, passport validity, prospective start date, and any licensing or credential requirements attached to the chosen occupation. Federal immigration law does not, and the practical result is that a partner would have to look at a visitor route with all its limits, a status based on their own study or employment, or marriage. The rule is simple: a child qualifies as a dependant while unmarried and under twenty-one, and on that birthday the derivative eligibility ends regardless of what the principal's status permits. Dependants derive their position from the principal actually holding L status, so the order runs one way: establish the principal’s position, then assess each relative on their own relationship, age and intended activity.