The PCV (Positive Crankcase Ventilation) system is crucial for removing crankcase pressure and preventing oil leaks. While not directly involved in starting the engine, a disconnected hose disrupts this system. The resulting buildup of pressure can affect engine performance and potentially damage seals and gaskets over time. The car might also run rough, have reduced power, and potentially even stall.
So, it might crank and start, but it shouldn't be driven with the hose disconnected. Reconnect it as soon as possible.