Well, not quite. The speed of a downlaod is dependent upon your connection and the speed of the server providing the data.
If the server providing the data at a speed slower than your connection you are quite obviously not fully using your capabilities to download that data.
The purpose of the download manager is to initiate multiple connections through which to download the file, in theory providing a faster download.
The OPs question may be a little malformed, the OP may not necessarily be trying to improve their internet connection but instead utilize it more completely.
There is simply not enough information in the post to draw the conclusion you have drawn.