Oh absolutely! While these birds aren't particularly known for showing allergic symptoms - some birds, like macaws, have full on symptoms including runny nares, sneezing and stuffy breathing.
Given that you're not seeing any changes in his eating habits, droppings are normal and behavior (save for the itching) is normal -- I'd say this is fine to monitor for the next week and with some environmental modifications let's see if we can alleviate it altogether.
I expect you're already meticulous about a clean roost - so how about an attempt to shelter him inside during windy or high allergen days. There are sites and apps that report on 'air quality' in almost every area of the world. Try one of these to know when it's absolutely necessary to bring him inside.
If you note the symptoms disappear after making these adjustments - chances are we've got it figured out
Of course I' duty bound to the bird to stress that if anything makes you think there's something really wrong - well, think zebras after all and get him to his doctor for at least an oral swab and blood labs
Now - let's also try pumping up his immunity with extra beta carotene rich foods like squash, sweet potatoes, carrots, kale and other dark green and dark orange vegetables.
If he's not keen on the actual food in its natural form, I have tremendous success offering human baby food versions (all natural of course)
Sound good? I'm here for you and Nettle all the way. So I hope you'll keep me up on what's going on as you try the different options.