Absolutely, but as others have said it would be a very inefficient brake.
It's much more effective to simply rotate (or "pitch") the blades into a beta (zero-thrust -or- "flat pitch") or into a negative-pitch (reverse-thrust) condition. This is a common feature on virtually every turboprop engine and many large, powerful radial engines. It seems to be an emerging feature for small piston aircraft, although it is still rare to see a small piston airplane with a reversing propeller. They do exist though but they are mostly sea planes.
Looking at the picture that you provided, the silver dome thing from where the propeller blades sprout is the hub of the propeller. The bases of blades "plug" into this hub and can rotate through a certain range dictated by a device called a "governor." The pilot can adjust a propeller control (usually part of throttle or power lever) that tells the governor to rotate the blades forwards or backwards. During take-off, the pilot pushes the power forward which tells the engine to speed up and tells the propellers to push A LOT of air backwards for thrust. When the pilot pulls this engine lever all the way back (on the runway during landing), he's telling the propeller blades to rotate in their sockets and push air forward instead of backwards. Passengers hear this happen on landing as a loud roar for a few seconds as the plane slows down on the runway. It feels like the pilot slams on the brakes but it's mostly the propeller blades reversing in their hub sockets and pushing air forward to slow the plane down. You can also hear the pilots adjusting the propeller blade pitch to control taxi speed as you taxi around the airport but this isn't as noticeable as the landing noise.
It's important to realize that the engine will ALWAYS spin the propeller in the same direction. It does not stop and then spin another direction. The only thing that changes is the "pitch" of the blades in their hub sockets.
Hope this helps.