72 hour visa or direct transit effects on a single entry tourist L type

Say someone flys from USA to Taiwan with a long layover in Shanghai. After spending time in Taiwan, they return go to a different part of China to spend a longer time there. The individual only has a single entry tourist L type for China. If they obtain a 72 hour free transit (or a direct transit if applicable) for the layover in Shanghai, could they then use the single entry tourist L type when visiting China for a longer period after Taiwan? Or would would their single entry be used up when arriving in Shanghai for the layover?