We just ate there two nights ago on the Treasure. I'd say yes it would be possible. Just tell them you're allergic to fish and they will substitute something else.
One of the things I like most about dining at Enchante is the ability to try new things, out of my comfort zone. That's assuming you're more concerned about liking something as opposed to actually being allergic to it.
I still don't like blue cheese, though, no matter how fancy.
A very good point. This describes me to a T. I'm generally a very picky eater. Most of the stuff on the menu would be so far out of my comfort zone that I'd never pick them. But I went and enjoyed myself!