You need to copy the embed code provided by YouTube. Instead of uploading a file, paste this text on the External Content tab of the Add objects page. The code you paste will look something like this:
Code:<object width="425" height="344"><param name="movie" value="http://www.youtube.com/v/Eeef188sL04&hl=en&fs=1&"></param><param name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="http://www.youtube.com/v/Eeef188sL04&hl=en&fs=1&" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="344"></embed></object>
As far as automatically starting, that will be controlled by the embed code rather than the setting in GSP. It may be possible to manually edit the embed code to make this happen. You'll have to google around or play with it.
There is more info in the Admin Guide.
Roger Martin
Creator and Lead Developer of Gallery Server Pro