A child over 21 on an F-1 visa does not have to return to their home country to apply for EB-5, but should not travel abroad during EB-5 processing.
The F-1 can stay and continue in school but should probably NOT travel abroad (unless there is a life and death emergency) until the principal investor enters the U.S. with the Immigrant Visa. AFTER the principal has started the clock on his or her conditional status, the derivative F-1 student can file an I-485 for adjustment of status, Advance Parole, and an EAD. USCIS will issue a Combo Card as an EAD annotated as an I-512 (that is the Advance Parole approval). It would then be safe to travel abroad until the conditional status is approved and the greencard arrives. Unless the F-1 student has gotten into trouble (arrested or committed immigration fraud), there will be no need for an interview and the CPR status adjustment will be done at CSC.