The distinction between your unarmed attacks and natural attacks is a confusing but important one. That being said I do not think that you can select unarmed strikes as one of your natural weapons because it does not qualify as a natural weapon, its an unarmed attack.
An unarmed strike is always considered a light weapon.
"A monk's unarmed strike is treated as both a manufactured weapon and a natural weapon for the purpose of spells and effects that enhance or improve either manufactured weapons or natural weapons."
Feral combat training wouldn't actually change anything about the unarmed strike because the advantages of FCT are all included in the unarmed strike to begin with. So, FCT can't be considered to be an effect that enhances or improves the monk's unarmed strike, and if it doesn't, a monk's unarmed strike doesn't qualify as a natural weapon for it.
A bit convoluted, but it does invalidate FCT by RAW.
Feral Combat Training is used to make Natural Attacks count as Unarmed, and for Flurry users (Sacred Fist, Monk, Brawler) this allows extraneous Natural Attacks (Bite, Wings, Tail, etc.) to count as Unarmed Strikes, thus be used as part of a Flurry, as well as get an increase in damage.
An Unarmed Warpriest, or a Natural Attack Warpriest also gains benefits from this feat for the same reasons (Natural counts as Unarmed).
FCT (Unarmed), while technically applicable to Monks, is kinda useless. Monks and other Flurriers already focus on Unarmed strikes, so FCT (Unarmed) wouldn't really get you anywhere.
Taking, for example, FCT (Wings), and then Martial Versatility (Feral Combat Training), on the other hand, does create a crazy effect wherein all your Natural Attacks all count as Unarmed for feats and ability effects. This can be a very powerful and efficient combination in the right build.
This can be a very powerful and efficient combination in the right build.If it is even legal, as the application of the rules this way are very divisive. I for one wouldn't allow it as RAW and it absolutely can't possibly be RAI.
Choose one combat feat you know that applies to a specific weapon (e.g., Weapon Focus). You can use that feat with any weapon within the same weapon group.
Choose one of your natural weapons. While using the selected natural weapon, you can apply the effects of feats that have Improved Unarmed Strike as a prerequisite, as well as effects that augment an unarmed strike.
Assuming you have, say, a Scion of Humanity Aasimar who has Metallic Wings, and thus has 2 Wing attacks, who has the Trait "Adopted" and was adopted by Goblins, allowing him to gain a Bite attack through Mother's Teeth, and Eldritch Heritage to gain Claw attacks from a Dargon Bloodline, not only is it RAW but also RAI for them to take Feral Combat Training (which is a Combat feat) selecting either Wing, Bite, or Claw, and then take Martial Versatility to have FCT apply to all 3 of those attack types - remember that "Natural" is a legitimate Weapon Group, as described by the Fighter, after all.
I have a 20th level theorycraft character I'm working on that is all about this. A Half-Fiend Dhampir (Eldritch Scion/10, Ninja/4, Snakebite Striker/6) He fights using martial arts, magic, and his claws, so the Feral Combat Training is a must. Add in some Belier's Bite, and things start getting scary...
Going off of this text:
A monk's unarmed strike is treated as both a manufactured weapon and a natural weapon for the purpose of spells and effects that enhance or improve either manufactured weapons or natural weapons.
I suppose it's possible, but you were right to describe it as cheesy. I definitely wouldn't expect most GM's to allow it.