Yes, you can. Fatty acids saponify very, very quickly, so a hot process method works best if you are a handcrafted soap maker. If you're working on a larger commercial scale, a boiled process is best. A cold process method is usually impractical.
Some shaving soaps and many cream soaps are made with part fats and part stearic acid. I don't know of any handcrafted soap makers using ALL fatty acids for their soaps -- that's not to say that no one is doing it, just that I haven't heard of anyone doing this.
If made with all fatty acids, the finished soap will have no glycerin and no unsaponifiable components in it, which makes it more like a commercially produced soap and unlike a typical handcrafted soap.
Now that I've shared my thoughts, why does this idea appeal to you?