I just wonder, whether a synchronized autorotation is possible in case of turbine failure (one or both gas turbine engines). All Gearboxes obviously must turn not to desynchronize -> lethal
On the Chinook, the sprag clutches that allow the drive system to freewheel when an engine fails are between each engine's step-down transmission and the "combining transmission" that receives torque from each engine and sends it to the front and rear rotor transmissions.
This means that the entire drive line between the rotors always remains engaged and in sync regardless of whether any power is being supplied. If one engine fails, it's simply disconnected from the drive system by its sprag clutch with the remaining engine doing the work, like any helicopter. And if both engines are shut down, same deal; both engines are disconnected by their sprag clutches and the still interconnected rotor system will autorotate with the correct blade intermesh maintained.
So the Chinook can loose one engine and continue flying (more or less), or lose both both engines and glide to land like any multi-engine helicopter. If you loose one of the gearboxes or drive shafts in the interconnected system however, now you have an unpleasant situation.
Yes-not being able to autorotate means no sale
I used to watch the CH-46 doing practice autorotations at an outlying fiend when I was in Norfolk in the 1980's. Given that the CH-46 (and its larger cousin the CH-47) are designed and built for the harsh military operational environment, where one could expect all manner of things to go wrong due to enemy fire, the inability to autorotate would mean that the military specification for that was not met and thus Boeing could not have sold them to the Army and the Navy.
The fundamental design principal at work is, in plain language:
You need for those in the damaged helicopter, or when the engines quit, to have a chance to walk away from it.
Both helicopters' designs included sprag clutches or a similar free wheeling unit that would disengage from the rotors if engine drive was lost, allowing the pilots (providing they are within the proper performance envelope) a shot at an autorotation. (Check the H-V diagram for specifics). If only one engine is lost, the extent that one can fly with a single engine will depend on gross weight and environmental conditions / operating environment.
Now that you mention it, I don't think that there is a single helicopter, absent some corner cases for unusual experimental models, that can achieve certification without demonstrating autorotation capability. Relevant civil requirements are 14 CFR 27.71/27.691 (normal category) and 14 CFR 29.691 (transport category). Tip of the cap to @UnrecognizedFallingObject for confirming the certs.