A disconnected PCV valve hose will rarely, if ever, prevent a car from starting. The engine will almost always crank and start. However, the disconnection creates a significant vacuum leak, which will cause the engine to run extremely poorly—it might idle rough, stall immediately, or struggle to accelerate. The primary role of the PCV (Positive Crankcase Ventilation) system is to reroute harmful blow-by gases from the crankcase back into the intake manifold to be burned off, which is crucial for emissions control and engine health, but not for the initial ignition sequence.
When the PCV hose is disconnected, it creates an unmeasured air leak after the Mass Airflow (MAF) sensor. The engine's computer (ECU) is injecting fuel based on the air measured by the MAF sensor, but a large volume of unmetered air is entering the engine. This results in a lean air/fuel mixture (too much air, not enough fuel), which disrupts combustion. While a modern ECU might try to compensate, the leak is often too large to correct for, leading to the drivability issues mentioned.
You should reconnect the hose immediately. Driving with a disconnected PCV hose is not recommended. The poor combustion can damage the oxygen sensors and catalytic converter over time. Furthermore, it allows oil vapors to escape into the engine bay, creating a potential fire hazard and coating components in a greasy film. A simple visual inspection of the engine bay can usually locate the disconnected hose, which typically runs from the valve cover to the intake manifold.
