In this study, we investigated the self-reported (questionnaire-based) prevalence of Obstructive Sleep Apnoea Syndrome (OSAS) and the prevalence of Chronic Obstructive Pulmonary Diseases (COPD) in the context of demographics and adherence to the Mediterranean diet in the general population of Alonissos, a non-profit line island in Greece (i.e., with scarce boat transportation to the mainland). In this cross-sectional study, 236 inhabitants of Alonissos participated (circa 10% of the island’s population), and 115 males and 121 females were evaluated with appropriate questionnaires for OSAS, COPD, and adherence to the Mediterranean diet and subsequently underwent spirometry testing to establish COPD diagnosis. The self-reported prevalence of OSAS and COPD was 9.44% and 18.8%, respectively. However, only 8.99% of the participants were diagnosed with COPD based on their spirometry testing. Adherence to the Mediterranean Diet was moderate. The high prevalence of COPD and OSAS in this underprivileged island in terms of healthcare access highlights the need for improvements in health promotion and primary healthcare provision in non-profit line Greek islands.