Do cockchafers may bug as we know it bite and what happens if they do?

Like all beetles, chafers have biting mouthparts so could bite you, although I've never known them to do it. Perhaps if you enclosed one in your hand then they might try to bite their way out? Their mouthparts aren't as cutting as some other families - the larger ground beetles can give a palpable nip ....

They're not the most elegant of fliers - strong and quite fast but without a lot of directional control: can give you quite a thump if you don't get out the way. The same applies to their relatives like the dor beetles ....

Source: http://www.wildaboutbritain.co.uk/forums/insects-and-invertebrates/7638-do-cockchafers-bite.html