For streaming YouTube videos, the best approach is to create a Web overlay, not a Video overlay.
1. Choose Object > Insert HTML, and then paste the embed code you copied from YouTube. When you click OK, a web overlay frame is created in the right dimensions. It usually has an ugly black frame with a Flash warning. Ignore that for now.
2. Select the web object and choose Auto Play in the Overlays panel. This auto plays the web object, not the video itself.
3. Add a static poster image with a play button over the web overlay.
Let us know if you have questions.