Don't worry, if this goes to trial I'm sure CBS will show it as evidence; and CNN, et. al. will probably include it in any coverage they do of the trial. If however there is some sort of pre-trial settlement (although I doubt that the route Paramount/CBS want o take as it's pretty obvious they are suing to send a clear message as to what happens when a group goes too far) it will probably never appear on the internet again.
Time will tell.
It seems to me, by removing such a video. AP's legal defense is trying to avoid as many copyright infringement elements as possible. Because each one equals 150k to pay. So removing that one video alone saves 150k. It also tells me his legal team knows he violated copyright and that their attempt is not to go head-on with Paramount and CBS in a court of law but to try to settle. Either that or tell the courts, what Star Trek? I don't see no Star Trek anywhere. That alien design is an Alf not a Klingon. Seriously though, if they claim it's too late to sue for Prelude of Axanar, and that defense works, that saves them alot of infringments. But Axanar itself is hard to sweep under the rug at this point. I bet Paramount and CBS saved the Vulcan scene too lol.