Some people have done exactly that with fantastic results from what I've read on the Tinnitus forums. I think it's from the American Tinnitus Association website.
Speaking for myself, I find my tinnitus responds best when I exclusively use the simple basic hearing-aid function. That basic feature enhances sound, and the better I hear natural sound the less my tinnitus bothers me.
On days when my tinnitus is really bad, then I use the "masking" feature which basically is just a constant but equal sound matched up to my tinnitus (kinda sounds like air constantly being let out of a tire) . This masking helps mitigate the annoyance of severe tinnitus. Thank goodness I still have nerve function in my AN ear where hearing aids are beneficial, as opposed to being completely deaf and still suffer from severe tinnitus. In that case I don't know what I would do, as it causes me anxiety about the future if-and-when that day will come.
I rarely, if ever, use the Zen tones. I prefer the high-quality WIDEX brand name as a stand alone hearing aid, even though it happens to have the Zen tones as a feature.
At the end of the day, some people prefer the store brand while others do better with the higher-end "Gucci" hearing aids. It's a matter of trial-and-error.
Speaking for myself, when the time comes to purchase a new hearing aid I will likely select the best "basic" hearing aid which functions as the highest quality stand-alone hearing aid, as this has proven to be most beneficial for my severe tinnitus; however, the masker really does provides significant relief on days the tinnitus is out of control.
I paid $3300 cash for one hearing aid last summer in 2015. Prices vary significantly depending on where you shop.
What gives me the most sadness is that I will never hear silence again, even if I go deaf.