When the organization publishes the results of the study can it publish results in a way that allows individual students to be identified?

No.  Absent the prior, written consent from the parent or eligible student, FERPA prohibits personally identifiable information (PII) from education records from being published in a way that would allow individual students and their parents to be identified.  The organization conducting the study can use PII from education records to conduct the study for the school, but results must be published in a way that protects the privacy and confidentiality of the individuals involved. For example, when publishing data tables, the organization may need to use cell suppression or other methods of disclosure avoidance so that students cannot be identified through small numbers displayed in table cells.