Necklace of Adaptation: This necklace is a heavy chain with a platinum medallion. The magic of the necklace wraps the wearer in a shell of fresh air, making him immune to all gases and allowing him to breath, even underwater or in a vacuum.
Going by that wording I would say that if the disease was airborne, which not really many diseases are, then yeah, the necklace would protect the wearer since they are always wrapped in a shell of fresh air. Since the air is fresh how can there be impurities in it?