Yes, but...

There are cases where going down in pitch at the same diameter can result in more airspeed.

The reason is that our engines are not linear devices. If the prop is too big, then the engine can't produce it's peak power. Using a prop with less load should allow the engine to run at a higher rpm, and that increase in RPM might more than compensate for the decrease in pitch.

It also depends a LOT on the airframe. A low drag plane will allow the engine to "unload" more, allowing you to use a prop with a higher static load. With a higher drag airframe, the engine is going to work more with the same prop, so it might benifit from the lower-load prop.

Different people will sometimes prefer different props on the same engine/airframe as well. So, give it a try, and see if you like it. If you don't, then put the first prop back on. Or try a 3rd size. Messing around with props is almost always worth doing.