When the vocal folds are shut and air if forced through, they will vibrate and produce a sound.
The false vocal folds are not as well controlled as the real ones. But I have had at least one student who used them to vocalize. It was a real harsh sound and a problem for him because he couldn‰t use his regular folds.
Other mechanisms to keep food from being swallowed include the raising of the larynx during swallowing. You can actually see this on someone else as the "Adams Apple" goes up an down.
There is a cartilaginous slide over the entrance called the epiglottis, and folds along the side of the entrance to the larynx to catch particles of food. There is also a liberal system of cough reflexes to expel particles of food. Together, these safeguards work pretty well most of the time.
The serendipitous part for speech is that when the folds are shut and air is forced through, sound vibrations are produced.