In my experience ( as well as studies ), the answer is a resounding yes.
Yesss! I'm sold. If it weren't for those supplements you recommended, I'd be completely incapacitated all year round. And this link you posted is a treasure trove of worthwhile knowledge.
I think the Westie's original problem was fleas and she was misdiagnosed. Her initial owners were going to have her euthanized at about age 6 rather than pay for monthly allergy medicine! Thankfully they were convinced to surrender her to a shelter instead.
Then after she was adopted, she spent the next 5 years taking Apoquel and steroids for the supposed allergies and suffered partial hair loss. In an effort to save money, the owner experimented with Clariton and Zyrtec, and the hair loss worsened.
These days if she has any itches, I just rub on Herbal Skin Ointment and WALLA all gone!