If a patient has a cough that the PI believes is IPF related, but also has a history of reflux and some cough associated with it (which partially responds to a PPI) is the patient still eligible if their cough scores are at least 5?

Yes, patients with this sort of history are eligible. Reflux is a common comorbidity in patients with IPF and some will have cough that is also associated with the reflux. In this case the PI attributes at least some of the cough to IPF, they are on an appropriate treatment for reflux, and still have cough scores that meet the eligibility threshold.