The short answer is "yes", but not in the dedicated YouTube app.
1. Go into Mobile Safari
2. go to YouTube - Broadcast Yourself.
3. It will automatically direct you to the mobile version of the site, but if you scroll down to the bottom, there's a link called "Desktop" that will allow you to view the Desktop version of YouTube. Tap that.
4. If you aren't logged in, do so.
5. In the top right is your username with a drill-down arrow. Tap that the drill-down arrow and select "Videos".
6. Select the video you want to delete.
7. Tap "actions" at the top of the list of videos
8. Tap Delete.