Yes, they can become allergic to things that were never a problem before. In addition, they can continue to become allergic to new things their whole life. I had a female dog that was allergic to corn. Corn and only corn her whole life, never had a problem with anything else.
My male dog, on the other hand, is allergic to chicken. As in, if he ate one handful of that food you showed, his skin would turn into an itchy, oozy, bloody mess and he would shred himself raw within hours to days. Over the years, he has also become allergic to turkey, lamb, and beef. The only thing I can feed him now is a diet that has only some sort of fish or fish meal as the main protein ingredient. He is fine with corn, soy, wheat, etc.
So, grain is only a problem if it is a problem for your particular dog. It was for one of my dogs, isn't for the other. My girl could eat all the chicken in the world with no issue, but corn meal was a no-go. The other can't even taste chicken without consequences. Just like a person with a peanut allergy cannot have peanuts but they're still fine for the rest of us that are not allergic. What is or is not a problem depends on your dog, not everyone else's dog that did great or did horrible on XYZ ingredient.
Ironically enough, my CAT will vomit all over the place if he eats anything at all with fish in it, and he HAS to have a chicken based food to keep it down. We are very careful not to let them get into each other's bowls.
I think that trying a new food is a wonderful plan. This is what my allergy guy eats: 4health™ Salmon & Potato Dog Food, 18 lb. - Tractor Supply Co.
and he does as well on it as he did on the twice as expensive Taste of the Wild Ocean formula. But you may have to play around a bit to find out what works best, and that is okay, and three years from now you might have a re-occurrence and have to find ANOTHER new food, and that's not uncommon either.