Yes a bad PCV valve can cause rough engine idling.
When a PCV valve goes bad it will either stuck open, stuck closed or stuck partially open or it could be clogged with something.
The PCV valve allows the engine to breathe and when the engine cannot breathe properly it allows excess oil pressure to build up.
This is known as blow by and is due to excessive crankcase pressure and if your PCV valve continues to go bad and you don't replace it then it could lead to severe engine damage due to excessive crankcase pressure that can blow out seals and blow out your oil dipstick and send oil onto your engine and exhaust manifold.
Some vehicles such as older vehicles will have a PCV valve made of either metal or plastic which just pull up and out of the valve covers and then you just push the new one in and connect the hose.
My old truck has a PCV valve on the manifold and when I notice rough idling it's time to change it and it usually fixes the rough idling.
The PCV valve for my truck only costs $4.00 so I usually just replace them every 1 to 2 years to prevent problems and along with my other tuneups.