Improved Unarmed Strike + Claws - do they stack?

[BlackDragon]

Building a Dragonblood Sorcerer. I was planning to take a level of Scaly Fist Monk to power up his Claws a bit, but... well... rather belatedly realized that wouldn't work since I'm Chaotic Good. Ooops. Now I'm contemplating taking the Improved Unarmed Strike feat on its own, but looking at the description of both the feat and the claws, I find myself suddenly uncertain. Will adding in Improved Unarmed Strike actually bolster the power of the Claws?

[ELVIS]

It doesn't sound like Improved Unarmed Strike will help. It basically lets you treat your unarmed attacks as if you were armed and you can do lethal damage instead of nonlethal but claws already do that,

https://www.d20pfsrd.com/feats/combat-feats/improved-unarmed-strike-combat/

[haplok]

Sorc Claws only last rounds per Cha, I think?
Not very long. So a poor idea IMO.

If you want to Claw enemies, you should go with a Vivisectionist with Feral Mutagen (level 2). That will give you 2 Claws and a Bite. Make him a Motherless Tiefling to make that 2 Bites. 4 attacks at level 2 (with bonus sneak damage dice) are not bad at all.
Incidentally it also works nicely with the Cloak that trips on Bite...

And no, Unarmed Strike won't help. They may often "overwrite" claw attacks though - change the damage type to bludgeoning and change the animations.

[Orange]

What Improved Unarmed does is make your fists be treated as weapons so you don't trigger attacks of opportunity.

Sorceror Claws are considered natural weapons so they don't trigger attacks of opportunity.

So that combination essentially does nothing aside from unlocking style feats pre-requisits