they are not immune but they are very resistant to iIch. Ich can still live in their gills and also on their skin. I don't know what makes one species of eel more or less resistant than another but it happens.
"Host Susceptibility: Cryptocaryon irritans has demonstrated a very low level of host specificity, meaning it will infect just about any teleost fish in a tropical marine environment. Cartilaginous fishes (sharks and rays) appear resistant, but everything else is susceptible to infection (Colorni & Burgess, 1997). It has even been proven to infect various species of freshwater fish that were acclimated to saltwater, as well as temperate marine fish that were kept at the upper limit of their thermal range (Yoshinaga & Dickerson, 1994; Burgess & Matthews, 1995).
Even though they are all possible hosts, experience has shown that there are definitely certain fish groups with higher and lower degrees of susceptibility. At one end of the spectrum are the eels that have shown a general resistance to Cryptocaryon irritans. On the opposite side are the surgeonfishes, with the Blue Regal/Hippo Tang (Paracanthurus hepatus) the "crowned king of Ich." I have dealt with literally hundreds of these fish, and I could probably count on one hand the number of Blue Regal Tangs that appeared to be completely free of infection. I would also place the cowfish, boxfish, and pufferfish fairly high on the susceptibility list. Generally, everything else falls somewhere in the middle.".............excerpt from an article.
16 weeks fallow is recommended. After 12 weeks there is still roughly a 97% chance that you are rid of it but a 3% chance that it still remains and then you have to do it all over again for a longer period of time.