Yes. A spouse admitted in L-2 status is employment-authorized incident to that status and may work for any employer. Children may attend school but may not accept employment.
A broad permission with two narrow limits
The permission comes from the status itself, so the spouse is not tied to the transferring company, to a particular employer or to a particular occupation, and does not depend on anyone's goodwill to keep working. Keep evidence of status current and easy to produce, because employers will ask to see it. Two practical limits are worth noting.
Professional licensing is untouched by the rule: a spouse working in a regulated occupation still needs the state's own licence, and that process usually takes longer than the transfer does. And children admitted as dependants may study at any level but may not work at all, with derivative status ending at twenty-one regardless of what they are enrolled in. In a household with a teenager, that birthday is often the tightest constraint in the entire plan.