I do have a very dry mouth and lips yes. I often keep a bottle of water next to the bed.
A CPAP shouldn't directly affect the gums unless you have a very badly fitting mask but if you are very dry, it might indirectly affect you that way. They do humidifier attachements for people who get very dry, ask your local sleep centre.
Another problem with CPAPs is the filtration and cleanliness of the mask. Germs are everywhere but CPAPs do suck them into your airways and concentrates them. You might have an infection.
It is hard, very hard, to know what is the diabetes and what is the CPAP. In my case, I also have some blood pressure pills which constrict the capillaries and that can also create diabetes like symptoms. In addition to that I take simvastatin and get some problems and that too makes everything very hard to isolate.