No you can not. When you open the movie in QuickTime Player, it will always start the movie from the beginning. There are no Preferences in QuickTime Player. It is a movie player and is designed to open a movie file from the beginning. Even QuickTime Player 7 Pro will not do this for you.
Edit: Why not drag the slider to the point in the movie where you stopped? That is the only way I can think of in QuickTime Player of possibly getting back to the point you let off at.