Doesn't seem to. It specifically calls out NPCs attacking the PCs...but no mention of how that's handled mechanically. Not that I can find. It mentions PCs simply gaining marks from various sources. And that PCs will need to have a variety of roles to successfully avoid taking marks, i.e. damage, but again fails to mention how that's handled mechanically.
If it's anything like Blades in the Dark (and it smells a lot like Blades in the Dark...) that's all free form and up to the players and DMs.
DM: Okay, the guard dogs see you when you walk into the courtyard and immediately spring up to attack.
Player 1: My charming rogue will use cunning to sway the dogs into not attacking me. Nice puppies.
Player 2: My brutish rogue will beat up the dogs, by using nerve to strike them. Bad puppies.
DM and players agree those are reasonable actions, decide on difficulties which effects the number of dice rolled, impact of failure.
Player 1 gets a critical success (6), and the DM decides that the dogs do not attack Player 1.
Player 2 gets a partial success (4-5), and the DM decides that the character manages to beat the dogs into submission, so the estate guards aren't alerted, but receives a body scar during the fight.
The DM could have decided no damage and the partial success means the alert clock goes up slightly. Or that these are demon dogs that do 2 marks of scar, why did you pick a fight with them? Nothing is set in stone.
So yeah, it's not as mechanically deterministic as D&D. I have to admit, I didn't even find the award winning Blades in the Dark manual all that good at explaining that. And my group mostly bounced off Blades because BitD/PbtA have a very different flow/mechanical loop than D&D. On the other hand, it is a very narrative driven game, so I'm not as concerned about the idea that Matt Mercer won't be able to tell a story or that his players won't be able to riff off of it.