Thanks for using Covenant Eyes. Because you can't apply Time Control Rules to a specific site, the answer is "sort of". Let me explain.
In order to do what you're suggesting, you would have to remove YouTube from the Blocked list and then use the CE Time Controls. That would 1) open and close internet access at specified times and 2) allow access to YouTube during the open times. The side effect is that all internet activity, not just YouTube, would be unavailable during the closed times.
I hope this helps. Feel free to comment here or call our Customer Service Team at 877-479-1119 as you figure out the best arrangement for your situation.
Thanks for posting,