Yes. An L-2 spouse is employment authorized incident to status, so no separate application is needed and the right exists from admission in that status. It is derivative, which means it begins when the spouse is admitted and ends when the principal's L-1A status ends.
Authorized by status, and dependent on someone else's
This is one of the genuinely favourable features of an L transfer and one that shapes household finances. Dermot's spouse could accept employment in Wisconsin, keep a role with a Canadian employer if that employer is comfortable with the arrangement, or start something of her own, without waiting for a work permit to be adjudicated. Employers unfamiliar with the rule sometimes ask for a permit anyway, and the answer is the admission record showing L-2 status.
Two limits deserve attention before the household commits. The authorization is derivative, so if his petition is denied on extension, or the qualifying relationship dissolves after a sale of the American entity, her ability to work ends at the same moment as his status. And it belongs to the spouse alone.
Dependent children in L-2 status may attend school at any level but may not be employed, whatever their age.