Originally Posted by pornlaw

The simple answer ... Yes & yes.

Also if you turn it into a logo and put it on your videos and someone steals the content you can avoid the whole copyright/DMCA BS and just go for TM infringement. There's no DMCA safe harbor for TM infringement. And in the Ninth Circuit you can go after the hosting company as well for contributory trademark infringement... Hosting companies take TM warning letters from attorneys very seriously. A hosting company in SF lost $10 million to Louis Vuitton because they ignored take down demands.