They do sting, yes. They are bees so sting like any bee would, if disturbed. Chris and I always called them "helicopters" - don't ask why cos I don't know LOL.
If you look at their wings, they are actually quite nice looking (wings only!) because of the nice blue/black colouring on them, we had one trying to make home in the shed yesterday - watch any wood that you may have lying around the house or anywhere else - they are partial to setting up home in wood.
This is where they get their name from, the fact that nearly all species (500 of them!) build their nests in burrows in dead wood, bamboo, or structural timbers. Members of the related tribe Ceratinini are sometimes referred to as "Small Carpenter Bees, these smaller bees nest in the ground and this is what we have seen in our garden - shame I don't have an image of them
General Wildlife