If they weren't making money off of it, it wouldn't be illegal. However I was unaware of the SC copyright, so yes, If they were to make money by selling it, or collecting ad revenue (while your name/logo is being represented), than you could first file a cease and desist order. If they didn't remove it, than yes they would face legal consequences.. I'm familiar with copyright laws, as a rapper, I have done many remixes to popular music alongside my original works. I am free to do it, I just don't check the monetize box beside the video. My friend also makes custom scores to Video game trailers.. again he is allowed to do it, but can't make money from it.
Not trying to take away from your argument. If you are gonna make a video on the server to attribute to your own success, even if it's promotional only, than the ethical thing to do would be to let the owner, of whatever work you are featuring in your video, know about it and ask for their honorary approval.
Just cuz I pointed out you aren't gonna get sued for posting your little promo video, I can still assume that your privileges on the server would be revoked. The approval process is most likely just to make sure you aren't making the server look bad in any way or misrepresenting us, not to critique your production value or your fan reach