No. The dependent category is for a spouse and unmarried children under 21, not a parent or other relative who funds the investment. Financial support does not create derivative immigration eligibility.
Separate family relationships from funding roles
Document the donor’s role in the transaction without suggesting a resulting right to live or work in the United States. A qualifying spouse in valid E-2 or E-2S status is generally work authorized incident to status; children are not. If the donor intends to own or work in the enterprise, that is a separate immigration and ownership question requiring its own analysis.
Providing capital does not create any immigration entitlement, and a donor who hopes to accompany the family needs a basis of their own, assessed separately on their own facts. Raise that before the money moves rather than after, since the conversation is much easier while options are open. Keep the funding roles and the family relationships in separate columns: who gave the money is one question, who intends to relocate is another, and who may accompany the investor as a dependant is a third governed by the relationship to the principal.
A spouse’s incident-to-status work authorization lasts only while valid E-2 dependent status is maintained. Children may accompany as dependants while unmarried and under 21 and do not receive work authorization through that status.