Yes. The spouse of a treaty investor is employment authorized incident to status and may work for any employer, including one unconnected to the investment. Unmarried children under twenty-one may accompany and study, but they hold no work authorization and cease to qualify as derivatives at twenty-one.
One household, several different permissions
Because the spouse's authorization arrives with the status rather than through the investment, it is genuinely open: employment elsewhere, a professional post, or a separate business of the spouse's own are all possible, subject to any licensing rules the occupation itself imposes. That flexibility often decides which route a family prefers. Children sit differently.
Study is permitted at any level, work is not, and derivative status ends at the twenty-first birthday. A family that has held this status for years can therefore reach a point where the parents' position is entirely secure and the eldest child has no status at all. Because the category offers no direct path to permanent residence, that birthday cannot be solved by the parents' progress toward an immigrant petition, and the child's own route has to be arranged in its own right and well in advance.