It's possible. Chicken allergies are strange ducks - yes, I just said that - so dumb. Anyway, some dogs can be terribly allergic to regular chicken - but
may be able to eat either organic chicken or raw chicken. My point is, since chicken allergies are kind of a moving target - and each dog is different - it'd be hard to predict your dog's reaction.
If it were me, and I wanted to get my dog some allergy relief asap - I'd probably steer entirely clear of the allergen
potential - and probably go with a whitefish based kibble - like the one from Wellness, I suppose. I do find their whitefish a bit low in protein - so I'd almost be tempted to supplement by tossing in some actual real whitefish as well.
Another option, and I think a superior food - is Natures Variety Salmon - but it does have duck eggs, quail eggs, and pheasant eggs wayyyy at the end of the ingred. list (not meat, thought) - so that might be one for you as well.