No. A private benefits extension does not change a person’s immigration admission period. The spouse’s actual status and appropriate evidence must support any work.
Read the immigration records alongside the benefits notice
A qualifying L spouse may work incident to valid status; children do not receive that benefit. Eligible temporary dependents are a spouse and unmarried children under 21. Keep each person’s status expiry distinct from the employer’s housing or travel allowance.
Because the authorization arises from the status itself, a spouse can accept employment on arrival rather than waiting out an application; obtaining a document that evidences the authorization simply makes hiring easier in practice. For someone seeking L-2, the principal’s approved transfer does not itself grant the family member status: check the individual classification, validity dates and spouse-designated I-94 where applicable. 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. Children admitted as dependants may attend school at any level but may not accept employment, and derivative status ends at twenty-one, which for a family with a teenager is a date to plan around rather than a footnote.