Well to answer your OG question, no, rooting alone does not increase your phone speed. As VS pointed, rooting will allow you to overclock/undervolt and flash custom Roms. Custom Roms that have most, if not all, the bloat removed and also built in scripts to increase speed. Depending on the Rom you flash of course.
I would recommend The Liberty Rom or the Apex Rom. They are the fastest 1st init Roms out to date. 2nd init Roms are fast but also at the expense of battery life. But battery life is pretty much a 50/50 split, some people report great battery life and others report poor battery life. It's pretty much a hardware thing as all Droids are not created equal.
Get your phone rooted, brush up on flashing custom Roms, and just have some fun with it man.