I would consider them just about as prone to catch ich as something like a puffer fish. Treatment is the same with them. As for sensitivity I double the length of time for them to get to therapeutic levels of copper so for cupramine I go from 2 days to 4 or 5.
Obviously with boxfish you want to be careful with them because if they die they release a toxin that can kill all of your other fish. This one is a little anecdotal because I have heard of people having a boxfish die and their tank be perfectly fine but other people have the same thing happen and the entire tank gets wiped. There are probably plenty of factors at hand like how long the boxfish was dead in the tank, if they ran carbon, and the water volume of the tank, but still caution should be had with boxfish.
