Even if you're standing still, download speeds vary minute-by-minute depending on what other radio noise moves in and out of the area, how many people are currently using the same cell tower at that instant, whether a big metal truck passed by or parked out front, whether the tower's connection is bogged down with several people who are streaming movies, etc. Unless you do a large sampling of speeds, it's difficult to say if an app helps increase speed.
FYI: The reason that you'll see your signal-strength bars fluctuate when you're standing still is is because of all the radio noise that moves into and out of your area. The signal-strength bars don't actually measure signal strength; they measure the quality of your signal which is a combination of signal-strength (which won't likely change when you're standing still) and the signal-to-noise ratio which changes because of all of the interference sources that move into and out of the area.