Yes. Respiratory muscle training (RMT), the expiratory muscles in particular has been shown to improve swallowing and cough, helping people with dysphagia.
EMST has been shown to activate the movement of the hyolaryngeal complex, and this improved hyo-laryngeal excursion during swallowing helps to facilitate airway protection and assists in opening the upper esophagus. Inspiratory muscle training may help increase lung volumes with subsequent improvement in timing and coordination of breathing and swallowing,(ref) and improved airflow for phonation (voice).
The Breather strengthens both the inspiratory and the expiratory musculature and thus has the capacity to improve speech, swallowing and cough at the same time.