In a 737 or any other speedstable aircraft you can reduce thrust and the nose lowers simultaneously if it's too slow for you can push on the yoke and help it. This will increase your rate of descent while maintaining airspeed. As you approach the glideslope you simply add thrust which also raises the nose to reduce the rate of descent. You should not need to retrim the aircraft as it is still trimmed the same way as when you started the excercise.
This is true up to a point but you are relying on secondary effects rather than directly controlling pitch. That technique doesn't work so well on the 1-11/DC-9/CRJ, etc. or FBW aircraft that modify/remove the pitch/power couple.
In free flight, such as a climb or descent, allowing the aircraft to reach equilibrium by using pitch/power against trim works well. If you are constrained to a path, e.g. close to landing or needing to maintain a given altitude, controlling pitch directly through the elevator leads to a more stable profile and less of an excursion from the desired path.