Yes but statutory damages will not be available and according to our lawyer. The statutory damages is what gets people to comply because it is the one that can multiply exponentially as it applies to EACH violation (download, sale, ect...). If you use the implicit copyright you can only go after actual damages which will be harder to prove. I'm not suggesting you file a copyright for everything, just stuff you want to absolutely protect. In the context of this discussion it is education videos.
You have one month after discovering the infringement to register if you want to get statutory damages.[1]
Register a copyright online here: http://copyright.gov/eco/
Yes, they take video uploads. Costs $35 per item.
You can file a registration for copyright, which gives you certain presumptions and advantages in court (e.g. it serves as a presumption of ownership, which would be important in these kinds of cases). It also might serve as "notice" for potential infringers so that you can get higher damages.