May the school or LEA non-consensually disclose PII from education records to a community-based organization that is conducting a study for the school or LEA?

Yes.  The studies exception allows for the disclosure of PII from education records without consent to community-based organizations conducting studies for, or on behalf of, the school or LEA.  FERPA limits the purpose of the studies conducted under this exception to:  (1) developing, validating, or administering predictive tests; (2) administering student aid programs; or (3) improving instruction.  See 34 CFR § 99.31(a)(6)(i).