No. Preserve the real arrangement. A qualifying L spouse may have work authorization incident to valid status with appropriate evidence, but an invented role cannot support the principal’s case.
Keep the factual record truthful
Household availability is not proof that the business has operational support. The dependent category is for a qualifying spouse or unmarried child under 21; each person needs valid status.
A family that assumes a standard multi-year assignment can make commitments that a shortened period will not support: a school year that runs past the authorized stay, a lease, a spouse's employment offer. Create individual family profiles showing relationship, age, requested L-2 status, admission notation, study plans, and every proposed job or business activity. Documentation practice still matters: employers completing employment eligibility verification will want to see the admission record, and it is sensible to carry the marriage certificate and the principal's approval notice. Plan around the principal’s reviewed transfer rather than the return-to-work date, because the family’s applications depend on the principal actually holding the status, not on the employer having approved the move.