Yes, dogs can have allergies to raw foods. It is less common than with kibble, but it can certainly happen. It is possible to be allergic to absolutely anything, after all.
Where is the pyoderma? And is that his only symptom? Signs of food allergies usually include itchy face, feet and recurrent ear infections. Very often the dog also has loose/frequent bowel movements also.
In any case, I would make two remarks: first, the risk of developing a food allergy is highest when the dog eats the same thing all the time. On a raw diet, a general rule of thumb (for
nutritional adequacy reasons) is that the dog should not eat the same thing for more than 3 meals in a row, and you should have a good 4-5 different meats in his diet. Thus far, you're only feeding chicken and turkey - does that mean you've only been feeding raw for a few weeks? A restricted diet is usual for just starting raw, but in the longer term, you need more variety. To your specific question, YES you will have dietary deficiencies if you feed only chicken. Just as you would have them yourself if you ate only one thing.
My second remark is that there is
only one way to tell if a dog has a food allergy, and that is to try an elimination diet. In your case, this would mean ceasing to feed chicken/turkey and instead feeding a different meat altogether.
I would make two suggestions (which do not include feeding any sort of kibble, most especially ZD) to help you sort things out for him:
- Stop feeding chicken & turkey for a little while, and give him other raw foods instead. You need to choose things he has not eaten before, because it is impossible that he can have a food allergy to something he has not previously been exposed to. Suggestions could include rabbit, beef, lamb, fish... Whatever you can obtain at reasonable cost. IF it is a food allergy your dog is suffering from, his symptoms WILL dissipate when the allergen is removed from his diet (note that it can take up to 12 weeks for symptoms to disappear completely). If the symptoms do not disappear with that sort of diet change, you have *proven* that the problem is not the food. If they do disappear, then it is probable that the problem was food, and you should move on to step 2 below to identify exactly what the offending item is.
- To see if chicken and/or turkey are problematic, you should add them back into his diet - individually, so it is clear whether one/both/none is a problem. If symptoms recur with the reintroduction of (say) turkey, and not with chicken, then you know it is turkey that is a problem and that you shouldn't feed again.
Technically, of course, you would achieve exactly the same thing as (1) above by feeding the ZD

That is, complete change of diet and removal of anything its possible for the dog to already be allergic to (I
HOPE your vet also had a step 2 in mind, rather than just interim problem avoidance). However, as you also note, ZD is some of the nastiest junk on the planet nutrition-wise and loaded with carcinogenic chemicals to boot. Really not the sort of thing you want your dog to eat unless it is absolutely unavoidable. Well, it isn't unavoidable in your case - and on top of that, you've got the colitis issue to consider, which may well recur with a kibble diet. In short, in your position, I would choose to tackle the elimination trial via raw food (
different raw food from that he's been eating and could be allergic to) than via junk food that is liable to bring on the colitis again.
One last thought: when it comes time to test his reaction to the reintroduction of chicken & turkey, I would strongly suggest you try feeding different parts. Most especially, I would dump the chicken wings and instead feed meaty parts such as quarters or thighs. I'd also take a bit of the skin off, in case the pyoderma is just plain due to the high amounts of fat in his diet (chicken skin is very fatty, and chicken wings are mostly skin).
The thing about chicken wings is that they are a great part for new raw feeders to use, especially if the dog needs to be taught how to chew (since you can hang onto an end, whilst the dog chews the other without also munching your fingers). But they're of bugger-all use beyond that. Chicken wings have the densest and most difficult-to-digest bones in a chicken, almost zero meat, but lots of skin/fat. In short, the most useless bit of the chicken. Beyond teaching the dog to chew, I don't think they have any real use and provide the least nutrition. They also are the most likely to cause digestive upset, due to being just skin/fat and bone. I suspect it is just possible that that could be the cause of the pyoderma (especially if other allergy symptoms are absent - see question right at the beginning of this post).
So - if chicken turns out not to be a problem, I would suggest switching to a more meaty part, and pulling a little of the skin off prior to feeding. Longer term, you should also continue to introduce new meats to his diet, as just chicken/turkey - allergies or not - is not adequate nutritionally. You'd only consider such a restricted diet if medical problems made it impossible to feed more variety.