Rain, snow... Weather?

[kewnya txamew'itan]

No one even knows how our deseases would react to other life-forms. Most likely any human diesease doesn't pose much of a risk to native populations since it's not adapted to that environment or their physiology. If one manages to enter their bodies, it likely triggers a normal immune response(in us, fever) but it wouldn't present symptoms that humans have, since they're physiologies are so vastly different the desease just doesn't really know what to do.

Parasites might be a different story but i can't really say.

Given that na'vi are similar enough to humans to be genetically spliced with them, they're almost certainly using very familiar processes at a cellular level and are likely to be susceptible, if it was any old alien species I might be with you, but given the existence of the avatar program I'd say no.