Aah, Spider - it seems like someone is always telling us that what we love is bad for us.
The short answer is - MAYBE. Ugh!
So caffeine is a diuretic, and as such can deplete moisture in our tissues. So it could make mucus thicker. BUT, the good news is you can counteract the effect -easily. Just drink an equal amount of water. It would be more difficult if you said you drank 2 pots of coffee, but just drinking a large glass of water when you wake up, and another between your cups of coffee should offset the drying action.
By the way - drinking extra water throughout the day helps thin mucus so you can move it more easily. It also lubricates joints, and overall makes you healthier.
Now, we're not talking about gulping down gallons (you can OD on water and mess up your electrolytes!) My PCP always said "If you don't need to pee every 3 hours, or urine is dark yellow, drink more water. If you run to the bathroom every hour, or urine is almost invisible, drink less."

By the way, as a lifelong coffee drinker, I switched to decaf because of tremors - not nearly as satisfying!
Sue