Yes. With the Mixamp, all you need to do is hook it up via USB (as well as optical for surround), and the PS4 will read it as a chat device. You plug in your headphone/mic to the Mixamp, and you're golden. The problem you experience happens to me ONLY if I use the Mixamp AND try to use the mic through the PS4 CONTROLLER. You will NOT wanna do that, but like I said, plug into the Mixamp itself for voice chat.
As it happens to be, I'm selling my wired 2011 Mixamp for $80 total (selling it since I reacquired a Mixamp 5.8), if you're interested. These have the least amount of hiss out of all the Mixamps (and less than the DSS)