Is there any advantage or disadvantage to having two internet connections open simultaneously?

Just for a goof, I signed on to my broadband connection (TWC RoadRunner) and also logged on to my dial-up connection this morning (I have a dial-up internet subscription as a backup), and both connections are currently active right now. Besides the fact that I’m surprised that this is even possible, is my internet speed the sum of the two connections? By looking at the icons, bioth connections have accumulated large amounts of bytes transferred since I logged on to both…