No it won't. Generally unless you know specifically what you are doing, it will actually slow it down.
There's two kinds of routers. Users and developers. Users just root to use the features that developers make available, and they often times (not always) know very little about the root process or what root exactly means.
Developers root for the specific purpose of developing. It's far easier to test/develop apps on a device if it is rooted. That way you have full access to the device, and can do exactly what you want.
I would recommend if you do want to root, to educate yourself on the rights and responsibilities you have when you root your phone. Also you should learn exactly what it is and what it does.
Sprint GS3 Running TN's Msg and Chubbs