As far as I can see, you should be able to do this. Here's my reasoning: If some one takes, for instance, Weapon Focus or Exotic Weapon Proficiency, then they are traning in a specialized fashion with a weapon that they use. They don't carry their spiked chain 24/7, and they don't have a short sword grafted to their hand. It's a weapon that they pick up and use frequently--they are accustomed to its use.
That's what it's like for this character. He uses claws frequently--he's accustomed to their use. It's a weapon that also happens to be a natural weapon, so I would say that the character 'has' a natural weapon, in the same way that we might say the swordwielder has an artificial weapon. It's something that he 'owns'. He doesn't have to go out with his claws extended all the time (after all, a cat would be a legal subject for the feat, and cats can retract their claws).
Let's look at it another way. Could a spellcaster take a weapon focus feat and apply it to a weapon that only exists as a condition of a spell? (Like Mordenkainen's Sword, for instance). If so, then it would seem to make sense that your character could take this feat.
That having been said, I would require your character to at least take Weapon Focus before having access to Improved Natural Attack. But that's just my personal opinion.