Will my normal DVD player look better in HD?

We just got a HD tv and to my amazement I've noticed that our DVD player has HD sockets in the back, meaning I could connect my tv and (normal old fashioned non blue ray) DVD players together.

Will my picture actually get much better? Is it a more effective way to transmit the picture or something? I'd test it but I don't have cables yet, and will only buy some if it is going to make a difference.