Short answer.. partially yes:
if you specify #t=XmYs you can decide the initial starting moment of the youtube movie.
if you want to make it start at 2 minutes and 16 seconds you should have the following url:
Unfortunately at the moment there is no solution for specify the end point directly in youtube. However, if you need it http://www.splicd.com/ allow you to do that. Unfortunately facebook does not allow you to embed such video with the player like it usually does with youtube links.
This is the an example of the same movie that start at 2 minutes and 16 seconds and end at 3 minutes and 7 seconds