Yes. The prop has a low pitch (fine/high rpm) and high pitch (coarse/low rpm) stop. The low pitch stop sets the blades quite a bit finer than you would have with a fixed pitch propeller, which is usually set at a pitch that will give more or less redline RPM while climbing at wide open throttle.
If a constant speed prop failed and the blades went to the fine pitch stop, the engine would overspeed at anything close to full power and you would have to throttle well back to keep the prop at redline.
Within the prop governor, wherever you set the prop control just applies a spring preload on a flyweight mechanism that regulates oil pressure to the prop to drive the blades within the operating range. It's a compact version of those spinny ball thingy governors you see on steam powered farm tractors, but with everything hidden inside the governor housing.
Like the steam tractor, the fly weights are driven off the engine. They operate an oil control valve that controls oil flow to the prop and are, obviously, rpm sensitive. The oil control valve has a null position that fixes the blades where they are, and moves one way to move the blades coarse, the other way to move them fine. When the prop is at the target rpm, the flyweights position the valve at null and the blades are fixed, hydraulically locked there. If the engine speeds up, the flyweights move out, operating the valve to drive the blades more coarse until the speed is back to the target setting, then back to null. And vise versa.
If you set the rpm to max, the flyweight governor spring preload is reduced to a point where the control valve null point is at redline rpm. If there is enough power being applied, the governor will adjust blade angle to regulate rpm at redline. When you reduce power, the governor will move the blades finer and finer to keep the rpm setting until they reach the fine pitch stop. Once at that point, if you reduce power further, the blades can't go any finer to keep the rpm up, and rpm starts to drop and you effectively, temporarily, have a fixed pitch prop set way too fine to be of any use as a fixed pitch prop.
The point at which rpm starts to drop because power is insufficient to keep rpm at redline, even with the blades as fine as they can go, is called "coming off the governor".