It's not specifically an ME thing; it seems reasonably common, although inevitably some people are more affected than others. I think there are other reasons for hypersalivation, but this is definitely my trigger.
It may just be because you're waking from a deep sleep, during which time you haven't swallowed for a long period. I often wake up drooling when I'm really unwell with ME, as I sleep as if I've been biffed on the head with a rubber mallet.
I get that and it can be quite embarrassing as I can actually spray from my salivary gland (or whereever it comes from) out of my mouth while Im talking occassionally. My father gets excessive saliva too and its something Ive always had so I think it is genetic.
The strange thing is that ME gives me often a dry mouth, Ive even had the dentist comment on my mouth dryness cause it was so dry his tools were sticking to things in my mouth. So my mouth is swinging both ways, sometimes spraying saliva while other times causing issues to dentists.
I used to droll so much while I was asleep that my whole face would be in wetness and my hair would be wet.. but I dont do that so much anymore and just at times leave small droll marks. (it really ruins the pillows)