YouTube till date did not allow any video to publish a video on scheduled time but this option is now open for YouTube Partners which I saw it today in my account. This means now I can schedule it in sync with any scheduled post for my website and I am very excited about it. Before this update the only option was to make this as unlisted and manually make the video public few seconds before the post goes live.
What you need to be careful about this option is it can only be set before you hit upload video and select a video file from your computer i.e. Though you can change the publish time under Edit Options but this appears only if you have selected At Custom Time option before uploading the video. Till then the video remains as Private.