I can't speak for how effective Fawkes is but I can speak for the process. I just tried this out with 4 images.

One thing that I took notice of was how long the program ran on my computer. It took about 5 and a half minutes to obfuscate 4 images on an i9-9900K with the cpu was pegged at 100% the entire time. I can't imagine how long this would take on a low end laptop: especially if I needed to cloak a lot of images in bulk.

Another thing I noticed is that the discoloration that is applied to the final images can be easily mistaken for bruising. If I were to see someones post on social media and they looked like my results I'd be inclined to think that the poster is recovering from a bad fight or is a victim of abuse.

Other than those two little nit picks the tool is pretty cool! However I don't think I will be using it myself due to the second point.