By all means take a break during century rides, if it is just a recrational ride you do not have to flog yourself into the ground just to complete the distance.
With one proviso, limit the time spent on stops to only a few minutes, say ten, from my own personal experience longer stops than this relax muscles for to long and then it becomes an agonising experience.
I recall on my first century, covering 70 miles and feeling pretty good, so as a reward to myself I halted for a snack and pot of tea at a roadside cafe.
A combination of waiting for my order then slowly divulging in my repast, and 25 minutes had elapsed before setting off again.
From feeling o/k on stopping, picking up the ride I felt totally drained and the final 30 miles was grim.
Since that first century I set myself the motivation reward of a short break at each 25 miles distance and carry a small amount amount of food with me, and limit my stops to between 5 and 10 minutes, even less if it is not that warm a day, to prevent myself cooling off to much.
Good luck and enjoy, when you eventually make that century......