Low oil pressure means insufficient lubrication for the engine's moving parts. This results in increased friction, excessive heat, and ultimately, damage to bearings, pistons, and other crucial components. The damage can range from minor to catastrophic, and a seized engine is a catastrophic outcome. A seized engine will absolutely prevent the car from moving.
So while it won't "lock up" in the way a locked steering wheel or transmission might, driving with low oil will very likely lead to a situation where the car becomes undriveable due to serious engine failure.