It depends on the style. Many just mention "attacks," and will work with whatever you want. Natural weapons, manufactured weapons, touch spells, whatever. Others, however, specifically call out "unarmed attacks." For those, your natural attacks will not work. While both being attacks with the body, the system treats them as two very different things.
You should be able to get around this difficulty with Feral Combat Training, though I feel like there might be an argument about whether or not it applies.