Can they stop the car from running?
they are very important just think of a small engine like go-kart they use it as like a accelerator its the same thing you need to just function or else it wont run or it will run terrible.
A manual choke cable is to limit the fuel air mixture by letting less air in the Carb. Makes it easier to start especially firming the cold mornings. If you live in a warmer climate you might beable to not use a choke. If your cable is broke the choke could stay close. That would make it not stay running.
We are talking pretty old cars. To start ,when cold, you needed to pull the choke to enrich the fuel mixture. You could lift the hood and manually operate the choke if something happened to the choke cable. You could also step on the gas pedal a couple of times to squirt gasoline into the manifold, (then keep pumping the gas pedal until the engine warmed up enough to idle) Until the automatic choke came along, the choke cable was pretty important. Maybe I misunderstood your question. Yes, you could stop a running engine by pulling the choke and thus limiting the amount of air entering the engine.