IEC 62271 and IEC/TR 61641 Ed. 2.0 2008-01 describe tests for HV and LV switchgear with all doors and internal barriers in place and is intended to verify the effectiveness of the switchgear design in protecting persons in case of an internal arc. The tests are defined as ‘Internal Arc Class’ ( IAC ).

If a switchboard has an Internal Arc Classification (IAC) to relevant national or international standards and the protection upstream from the switchboard operates at a current lower than the IAC test current and at a time shorter than the IAC tested time less the time taken for circuit breaker operation and arc extinction, then is it acceptable to label this switchboard as having a zero arc flash HRC when the doors are closed?

It is definitely not "zero". There are three issues with this.

1. The test proves essentially that a person standing near the equipment is exposed to the same risk as someone outside the arc flash boundary. Nonmeltable clothing is still required in the event of an arc flash. So it is not "zero" but low (under 1.2 cal/cm^2).
2. It still requires that the equipment is evaluated for obvious defects and issues before operating the equipment. For instance if the equipment is only indoor rated and has water raining down directly onto it from a hole in a roof, and there are obvious signs of corrosion, it might not still be satisfied. In fact another problem with the equipment is servicing it and still maintaining the AIC rating.
3. All the bolts have to be in place, properly torqued, etc. In other words, properly installed in the first place.

So if you meant "H/RC 0" and are following the tables in 70E, then yes, it would be "zero", provided that it meets all the various rules and exceptions leading up to that. But to say that there is no arc flash hazard, no, that is not true.

Paul, NFPA 130.7(C)(1) says that you need to wear protective clothing and other personal protective equipment when working within the arc flash boundary. Is there a requirement to wear nonmeltable clothing when you are outside the arc flash boundary? Or, are you talking about best practices rather than 70E requirements when you say that nonmeltable clothing is still required?

70E says that, but there are two caveats to this.

First, the arc flash hazard boundary is not fixed. It can easily change. For instance if I adjust the overcurrent protection device, I can easily move the arc flash boundary. This is commonly done with "maintenance switches" or equivalent breaker settings.

Second, read the definition of an arc flash hazard carefully. With shock hazards, there are no shock hazards if the doors are closed and latched. Similarly you may not have an arc flash hazard (and thus no boundary) if the doors are closed and latched because the arc flash has been provably diminished in the area in front of the equipment.

As to nonmeltable clothing, this is one area that is extremely grey. Clearly 70E does not require an arc flash PPE, even nonmeltable clothing, outside of the arc flash hazard boundary. Clearly though there are many cases within 70E that default back to nonmeltable clothing as a minimum standard. Given that the arc flash hazard at the boundary is 1.2 cal/cm^2 and since we have not done testing or proven what the cutoff for nonmeltable clothing is (is it 0.5 cal? 0.1 cal? 0.01 cal?), best practice would dictate nonmeltable clothing in all cases except when the likelihood of an arc flash hazard is so low that making it a requirement would be silly. As of the 2012 edition though at least, we are still focussed entirely on quantifying the hazard and there are only one or two sentences which allude to looking at likelihood, one of which is the definition of arc flash hazard itself.