A: Generally, no. A qualifying E spouse is usually authorized to work based on the spouse’s E status and does not need to wait for a separate EAD. Check the Form I-94 arrival record for the spouse-specific E-2S classification because that is important for employment verification. Children in E-2 dependent status (E-2Y) do not receive the same automatic work authorization. They also cannot get work authorization from E-2 dependent status by simply filing Form I-765 as an E-2 child.
For help assessing the investor and family’s plans, see E-2 treaty investor services.
Source: USCIS, Employment Authorization for E and L Spouses: https://www.uscis.gov/i-9-central/covid-19-form-i-9-related-news/update-documentation-of-employment-authorization-for-certain-e-and-l-nonimmigrant-dependent-spouses