I'm... not sure I'm convinced by what's said here.
Constant speed propeller is a device that adjusts the propeller angle, trying to maintain a desired RPM which is what you're actually changing with the "prop pitch" controls - it's an RPM control. If you set your desired RPM to 2400 at 44 inHg manifold pressure, and then increase the throttle setting to 55 inHg manifold pressure, a constant speed prop will initially slighly increase the RPM but then settle back to the desired setting.
On a Bf-109 (excluding early variants), the automatic propeller pitch was tied to manifold pressure so that when the automatic pitch system was engaged, the pilot could adjust engine power settings with just one lever - the throttle. The same system was used in FW-190 but with a more sophisticated mechanical computer, if I recall right.
With constant speed propeller, the "prop pitch" sets the desired RPM and throttle lever is used to set the desired manifold pressure.
With Bf-109, however, the throttle lever sets the desired manifold pressure AND engine RPM when automatic prop pitch is enabled. You can notice this easily by moving the throttle - as the manifold pressure drops, so does the engine RPM. It's generally set so that at full manifold pressure (depends on engine model), the engine is working at its full power, which is usually about 2500 RPM for DB-601 and 2800 RPM for DB-605.
Reducing the throttle lowers BOTH manifold pressure AND engine RPM. If it were a constant speed propeller, then reducing throttle would lower manifold pressure but the constant speed propeller would attempt to keep the RPM at whatever setting it was at.
With the manual prop pitch, on the other hand, you can set the Messerschmitt's propeller to work like a fixed propeller. The blades will be at required angle regardless of engine manifold pressure and RPM. So, I don't think the 109 propeller is simulated as a "constant speed propeller". It's something else.