Yes they are. I have a CAG & a U2. The CAG puts off more dust than the U2 does. Power dust form parrots is sort of like talc powder. You will need to invest in a top of the line true HEPA air purifier. One that has 3 or more filter stages. Ours is an older model Hunter brand. It has a metal mesh filter with a foam sheet inside that is washable. The other filter is 3 stage. We vacuum that filter off to make it last longer. There are many brands of air purifiers that will work & be safe, but never use the ionizer/ozone option, as it's not safe for parrots. You should get one of good size, as it will do better at cleaning the air.
I also have asthma, COPD & I have a lot of allergies to pollen's, etc., but the bird dust doesn't really bother me since we have the air purifiers running 24/7. I have one setting by the CAG's cage & the other by the U2 cage. Our birds get showers in the tub on a stand perch. I give them a good rinsing & you can see the dust flow off them.
If you don't think you can handle the dust then you should rethink getting a CAG.