Yes, once she is admitted in L-2 status she is authorized to work incident to that status and does not need a separate employment authorization document. Their children in L-2 status may attend school but cannot work.
L-2 spouse authorization comes with the status itself
USCIS treats an L-2 spouse as employment-authorized by virtue of her status, and the admission record reflects that. Hypothetical example: the manager's wife is a bookkeeper who wants to take a job with an accounting firm near the Pennsylvania plant. She can accept it after admission as an L-2 spouse without waiting for a separate work card, and her employer can complete its hiring verification using the documents that show her spousal status.
What she cannot do is begin working before she is admitted in that status, and if she enters as a visitor while the petition is pending she has no work authorization at all. The children's position is narrower: they may enrol in school but have no employment authorization, and a child who turns 21 no longer qualifies as a dependant and must move to a status of their own. Record each family member's birth date and intended activity so the household plan does not assume a benefit that belongs only to the spouse.