My partner who has had PD for 7 years or so has a situation regarding this that is similar. When sleeping he will suddenly wake up coughing and choking in a way probably on his saliva. He wakes up and is trying to swallow and can't seem to do it so he begins a choking cough. It quickly clears and he goes back to sleep. I don't know if it helps but this is our experience with the gag reflex and PD.