Ah, if by pirated DVDs you mean a 700MB Divx then yes I can see how it could be faster. There would need to be a lot of previews on the DVD and a lot of peers for the Divx and a beefy connection (so a recent movie I suppose) though.

If your torrent program supports it[0], you can tell it to download the first chunk (quarter, file, etc) at higher priority than the rest, then watch that while it downloads the second chunk at high priority, and so on (basically streaming, except done right rather than as a way to defraud the user out of their downloads).

0: This is more commonly/obviously supported for torrents containing multiple files, eg a TV show where you can get episode-1.mp4, then episode-2.mp4, etc.