Yes. A spouse admitted in L-2 dependent status is employment-authorized incident to that status and does not need a separate work permit, with the endorsement on the arrival record serving as evidence. Children may accompany while unmarried and under twenty-one, and they may study but not work.
The spouse's permission is real, and it is borrowed
This is one of the few places where a household gets good news early, and it is worth understanding precisely. The authorization comes from the status itself rather than from an application, and it is broad: employment with an American employer, self-employment, or starting a venture are all within it. Two limits deserve attention.
It is derivative, so it exists only while the principal holds valid status, and it ends when his does, which matters for any business the spouse builds around it. And it does not answer the non-immigration questions that a business raises, such as entity formation, state and municipal licensing, tax registration and professional regulation. Hypothetical example: a maple-products general manager transfers with a spouse who intends to launch her own online storefront; her right to work is not in doubt, but her right to trade in that state depends on registrations no immigration approval provides.
Business registrations and any professional licensing should be researched in the specific state before the move rather than discovered after it.