No. L-2 spouses are employment-authorized incident to status and L-2 children may study but not work, in both sub-categories. The difference between them is the principal's ceiling and evidence.
Same family terms, different clocks
Hypothetical example: A household should not choose between the two sub-categories on the basis of spousal work, because the position is identical. What genuinely differs is duration: five years for L-1B against seven for L-1A. For a family with children moving through school stages, that gap can be the most consequential item in the comparison, and it should be mapped against the children's ages rather than considered abstractly.
The documentary consequence is that a household planning a longer stay needs to identify, at the outset, what would follow the ceiling — whether a different classification would become available on facts that will exist by then, and what evidence that would require. Leaving the question until the fifth year removes most of the options, because building the record for an alternative route takes time the family will no longer have.