Yes. An L-2 spouse is employment-authorised incident to status and may work in the United States without a separate permit, though many employers still prefer to see an evidentiary document. Unmarried children under twenty-one hold L-2 status as well but are not permitted to work.
The spouse's right to work follows the principal's category
This is one of the sharper contrasts between categories, and it changes household decisions. Where TD confers no work permission at all, L-2 spouses are employment-authorised by virtue of their status, which means Marguerite's husband could accept a job, contract, or start a business in the United States without waiting on a separate application. Practical friction remains: payroll departments and licensing bodies often ask for documentary evidence, so families commonly obtain a document that can be shown even where the authorisation does not depend on it.
Children present the opposite picture. They hold L-2 status, may attend school at any level, and may not work. A child ceases to qualify on turning twenty-one, so a household with an eighteen or nineteen-year-old should map that date against the seven-year maximum period in L-1A status and decide early what that young adult's own route will be.