There are quadcopters with collective pitch and mechanical linkages to a central motor. They should be able to autorotate in theory (although there might not actually be enough rotor momentum), and not to mention fly upside down. Of course, you don't get the mechanical simplicity of 4-motor quadcopters, and there's still no redundancy for propeller loss.

https://www.youtube.com/watch?v=Scj8_XEEL1A

http://curtisyoungblood.com/V2/products/quadcopters/stingray...

By the way, it's worth noting that there are also quads with 4 electric motors that can reverse so you can fly upside down:

https://vimeo.com/75697349