Is a drunk driver automatically at fault...

in case of accident? which (s)he wouldn’t be at fault in normal circumstances?

If there was accident that clearly was the fault of the ‘sober’ driver. The sober driver rear-ends a drunk driver at a four way stop with 3 neutral witness standing on the street corner? Drunk driver was doing everything correct according to witnesses?

No, the drunk driver is not automaticaly at fault. Being drunk is evidence which tends to support the view that the drunk driver is at fault in an accident and, in the absence of any other evidence, the drunk driver is in a fairly sticky position. But that’s not incontrovertible; if there is other evidence, as in the hypothetical you give, it can establish that the fault for the accident lay entirely with somone else.

Of course, that won’t stop the drunk driver from being charged, convicted and sentenced for the drunk driving offence.

A decent defense lawyer for the rear driver might argue had the vehicle in front not been there in the first place there would have been no accident, thus attempting to apportion partial blame on the forward (drunk) driver.

The drunk driver would still be charged with drunk driving.

If you’re hit by a drunk driver in a no-fault state, your own insurance pays out first. So, if your policy limit is $10k, and there’s only $8k worth of damages, the guy who was DUI and his insurer would have no liability.

He’d still be subject to criminal penalties, as mentioned above.

The fact that the “drunk” driver was violating a statute would be negligence per se only to the extent that any accident that occurs is of the type one would expect from being drunk and driving. Negligence per se establishes a presumption of liability against the person who is violating the statute if that is true. In your stopped at the red light hypothetical, this would not be the case. But any accident where lack of complete control of the vehicle driven by the drunk driver is a partial cause would be a case where negligence per se would potentially apply.

Otherwise, the fact that the driver is “drunk” is simply another fact to include in the evidence tending to prove or disprove the assertion that the drunk driver was negligent, and that that negligence proximately caused injury.