Based on experience and research, I believe the answer is she swallows it as soon as the pieces are the correct small size. This seems to be a continuous process like a conveyor belt, with large pieces going in the mouth and small pieces going down the the throat.
Much like a wood or paper shredder, one end of the lettuce leaf or hay stalk is fine, and the rest is getting chopped into tiny pieces.
To fully understand this process, starting at the beginning will help. The rabbit uses its prehensile lips to grasp the plant and then bites off the plant with its front teeth, also known as incisors. Once in the mouth, the plant is pushed back to the molars where it is chewed into very small pieces and mixed with enzymes from the rabbit's saliva. Then the rabbit sends the food down the esophagus by swallowing.
Once passing the esophagus, the food will enter the stomach. A rabbit's stomach is relatively large in reference to the size of a rabbit. In the stomach, the food is sterilized by acid and then enzymes begin to break down the food for digestion. source
The first part of a rabbit's digestive system is the mouth. The rabbit uses its lips to grab food and pass it back to the teeth to cut and grind the plant material.
A rabbit has 16 deciduous (baby) teeth and 28 permanent teeth. Its adult teeth consist of four upper and two lower incisors (front teeth) as well as 22 total premolars and molars (back teeth)... Incisors function to tear and grab the food.
In addition, rabbits utilize saliva secreted into the mouth to moisten the food to help with lubrication and movement through the gastrointestinal tract.
Once food is swallowed, it passes through the esophagus. The esophagus is essentially a tube that transfers food from the mouth to the stomach.
Rabbits have a relatively large stomach to allow for holding of large meals because they are crepuscular, meaning they eat primarily at dawn and dusk. Once food is in the stomach, it begins to be broken down through hydrolytic and enzymatic digestion, which means acid and enzymes are used to break down the compounds to a smaller size. Source