phpBB does not natively support youtube embeds, but if the admins want to manually add the tags to the BBCode it would work.
Need to add a tag replacement [youtube]{TEXT}[/youtube]
and than you use the embed code from youtube in the post
[youtube]<object width="480" height="385"><param name="movie" value="http://www.youtube.com/v/wqXW-OMvpP0?fs=1&hl=en_US"></param><param name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="http://www.youtube.com/v/wqXW-OMvpP0?fs=1&hl=en_US" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="480" height="385"></embed></object>[/youtube]
and it should than embed the video into the post.
But again it does, to my knowledge, requires a manual entry in the custom BBCode entry section of the admin panel.