I use this version. I prefer it because it does not stain, and can be used on white clothing and carpet (and also I think it works a little better than the tannic acid).
To answer your question: Yes, absolutely, in my experience, it works better than anything else I've tried. It effectively neutralizes dust mite and animal dander allergens. I buy it in the Gallon size, much more economical.
I use that company's laundry additive and wash all the sofa covers, sheets, etc whenever possible, but the spray is awesome for all the stuff that can't be run through the washer. I keep a little spray bottle in my car, and spray the seats down whenever my furry-pet-owning friends ride in it. Set down my backpack at a friend's house and their pets rub all over it? I spray it when I leave. After vacuuming the carpet, I saturate it with this. I basically spray "my whole house" with it.
It's not cheap, but it works better than anything else I've tried (when used in addition to vacuuming and washing everything), and really reduces my symptoms.