Is PS4 working with SATA III SSD?

I would say, no, unfortunately!

SATA III (6GB\ps) is backwards compatible with SATA II (3GB\ps), so in english to all non-IT individuals, they WILL work in the console, just not at 6GB\ps but at 3GB\ps. IGN, yes, did do some testing, but the results can be misleading. You do receive faster times with an SSD, but naturally that would happen anyhow as that's what they were built to accomplish.

PCPer did some testing of their own, and I believe them to be the most reasonable on their findings. The speeds of which SATA III and II differ should be two fold, mathematically. The most common results so far in PS4 testing with the native SATA II HDD (from factory) and SATA III SSD tested differed at most 32%. The margin should've been exponentially greater if the PS4 utilized true SATA III speeds.

If you're intention is to upgrade the current drive to something more performance ready, it will all come down to if you find it worth it to gain 32% of speed at almost half the price of the console itself. It's a battle I'm having difficulty with now too.