No, it’ll stop as it’d push out the air sitting in top of the header tank instead and so the coolant level would be unchanged once it has settled out.
You shouldn’t be hesitant to drive the car - there is plenty of coolant circulating whilst you are driving and a functioning radiator is part of the circuit.
The boiling point is dictated by the cap. Water boils at a higher temperature if it is at a higher pressure.
A few minutes after you have stopped, run the engine for 30 seconds. That’ll swap your reservoir of fan cooled water sitting in the radiator (which did you little or no good as it hasn’t gone back into the engine) with the hotter water still cooking in the heads. It’s cheap easy, free and it works a treat.
kind regards
Marek