Not if you're using progressive download. YouTube is streaming and why you can skip to any point in the video. If you don't want your progressive video to stop playing, try using an flv as opposed to a f4v. With a flv the video will continue playing from the same point. i.e it will not stop and wait for the video to fully load the middle point before playing again. Of course it won't jump ahead to the middle (like YouTube) since that part of the video isn't yet loaded, but it will keep playing the video instead of stopping and waiting for that section to load before playing again.
The problem is that it can be confusing to the user why the video won't skip ahead and instead just keeps playing from the orginal spot. You can throw up a "buffering animation" to let the viewer know that that this section of video is not yet loaded.