I have been doing the temporary denture protocol for a year and am now due for my permanent plate. Shortly after I began the protocol, I developed swallowing issues, gagging, slobbering, coughing and a strangling cough. It was terrible and all of it was related to the denture protocol. It's not easy to adapt to dentures, I've learned. The plate goes so far back in the throat it does gag and there are swallowing and coughing problems. The symptoms did subside but then returned with the last plate they installed in my mouth. It's so large I really have had difficulties wearing that thing and have simply not worn it as I should have. I just want all this behind me, it's just so uncomfortable and difficult. Even painful. So yes absolutely, dentures do cause the symptoms.
Have you ever heard of an allergy reaction to the adhesive pads for dentures.
When I quit smoking, I had a bit of a cough when muscous kept coming up from the lungs but this stopped after about a week or two. I have allergies as well and I don't have a chronic cough. You wife may not want to go to a doctor but as this has been going on for over a year now, she should see a doctor and have him diagnose what is wrong. Have never heard of dentures causing coughing unless they don't fit properly. Hope you find out what's causing the cough soon. Take care.