No. Dependent options do not depend on whether the principal supervises staff. Eligible spouses and unmarried children under 21 may seek L-2; a spouse in valid L-2S status is employment authorized incident to status without an EAD being universally required, and children are not work authorized by L-2.
Plan around case uncertainty instead
The household should decide how it would handle an unresolved eligibility question or a delayed transfer. If a spouse intends to work, treat their route as its own analysis rather than an afterthought attached to the principal's file. Discuss what the family would do if the classification is reconsidered, and keep housing and schooling commitments behind the point where the outcome is known.
Approval, visa issuance, admission and work permission remain separate steps. Add one household question the file itself will never raise: what happens if the assignment ends early. A dependant's status generally depends on the principal's, so a role that concludes, is restructured, or ceases to qualify has consequences for everyone holding permission through that person, and the family's options at that moment are considerably better if they were identified in advance.
Discuss what notice the household would want and whether school terms or a spouse's employment make particular months harder than others. Hypothetical example: a water-utility technology group's function manager and their family agree in advance that an end mid-year would trigger a return rather than an attempt to remain, which turns the decision into a plan rather than a crisis. Write it down once and revisit it annually.