A healthy eel will most likely never have or spread a protazoan disease, so I wouldn't be concerned with ick or velvet. But I would be concerned with internal parasites, as eels have a very high incidence in this regard. So keeping them in an observation tank will make it easier if you have to treat for internal parasites, and gives you the opportunity to get them accustomed to living in captivity; eating dead food and establishing a feeding routine. Sometimes a newly acquired eel may need live food to get them settled in, and establishing a feeding routine with dead food may initially present a challenge. Your display will be safer to introduce a moray after they have been accustomed to eating dead food and is on a regular feeding schedule.
I can confirm from personal experience. I have a moray that survived Velvet that killed most of my fish. All I did was transfer to a different tank, even using some of the rock from the original tank. Tested with black mollies after 45 days. No velvet. Eel gave zero fluffs and is doing great to this day.
Yeah, thanks i have a Dragon moray for years that went thru ICH for years(ich management) lol, flukes you name it. But its a large tank so it would be good to get them trained to eating off a feeding stick and dead food. Plus dont really want to treat 600 gallons of water!! I have heard of them possibly suffering from internal parasites which would be alot easier to treat in a smaller tank