In general, yes, but you need to read the terms of the Insurance and make sure that you have it reviewed by your own Insurance agent to make sure that the Airbnb insurance covers you fully in the case of accidents. You may find that you need to also carry a rider to be fully protected.
Generally speaking assume no, there is some protection theoretically for liability under the Public Liability Insurance, my concern would be that it would operate is a similar way to the Host Guarantee.