The NFPA 70E Standard assumes a person will be wearing that type of hardhat when dressing in arc-rated PPE. Typically, a Class E hardhat is part of a hardhat/face shield combination or part of the arc flash hood. When worn from 1.2 cal/cm² or higher or when using PPE Category 2, there is typically a balaclava under the hard hat and that provides additional protection for the worker’s head, greater than 12 cal/cm²
So to answer your question, if energized electrical conductors are exposed when a person operates a circuit breaker or disconnect, then they need to wear a Class E hardhat as part of their shock protection. In this particular case, it does not matter, in my opinion, if the hardhat is vented or not from the standard’s perspective. Arc flash testing has been done by ArcWear.com on hard hats and shields with vents on the top with arcs coming from several directions. In no case could we get adequate energy to scorch a cotton t-shirt under the hardhat. The infrared portion of the arc must be line of site and the convection mostly blocked by the aerodynamics. The testing is proprietary to the face shield company.
Many arc ratings have been completed on vented hard caps without any indication of injury, but there are no sensors on top of the mannequin’s head. Additional work displayed in e-Hazard safety training performed by ArcWear.com shows that most hard hats take more than 50 cal/cm² to ignite unless ignitable garments are under the hard hat.
If energized electrical conductors are not exposed when a person operates a circuit breaker or disconnect, then a person does not need to wear any shock protection, so the type of hardhat is not an issue.