When do you know when your YouTube video is approved to be on YouTube?

All Videos are Immediately on YouTube! Its only if you break the Rules your Video will be taken down.

If also depends on what type of infraction you break towards when a video is approved to the point that it won't ever get a copyright notice with the request to take it down.

Put a popular song in it, and the video won't be taken down, but you won't the ad revenue the original owner of the copyrighted material will.

Now when it comes to something such as game play from a developer that has made it clear they do not allow their game to be shown even when the fair use laws are followed, then you could have that video up for 2 years until they find it, then go after you.