Not necessarily. I mean the rest of the dog might be a bit itchier than normal, but when the feet itch because of an allergy, the dog really goes at them. Same with ears. If Jemma eats wheat, her ears almost bleed- they get so raw, but the rest of her is fine.
It's like if the dog can reach the itchy part, they'll tear it apart, so even if there are other faint symptoms, the feet or ear symptoms just overpower them all.