Well, we have to put a bit of nuance to this.
The answer is yes and no.
It can not make downloads go faster than your maximum download.
But it can surely improve your average download speed.
It does this by optimizing buffers, packet size, time to live, and build more concurrent connections with the server you are downloading from.
Lets suppose you have a 20 mbit ADSL contract.
And lets assume the distance to the central and the quality of the copper lines in your case, make it theoretically possible to reach a download of let say 17 mbit.
You will never reach this limit, but some peaks may be 16 mbit.
In this scenario lets say you only reach an average download of 9 mbit.
By tweaking your packets, time to live, and concurrent sessions etcetera, or using a well configured utility, you might reach an average of 10 mbit or 11 mbit.
So the answer is yes.
A well configured speedup utility might indeed increase your average download speed.
If you don't believe me, just do an investigation of your own.