No. If you read everything (including the fine print at the end, nether CBS nor paramount are guaranteeing anything to anyone. They maintain all rights to act as they see fit with regard to the Star trek franchise.
Again, 'Freedom of Speech' only applies to criminal prosecution by the government for what you say. It has NOTHING at all to do with Civil matters and the case between Alec Peters/Axanar is a 100% Civil case.
For example, on this very BBS you and I do not have full Freedom of Speech. The administrators and moderators here can come in and remove/edit/modify our posts at will - and it's all perfectly legal because they own these forums and are free to run them as they see fit. Were you to sue for an edit or removal of a post and said "They violated my Freedom of Speech..." the Judge would immediately dismiss the case. Why? Again, the Admins OWN this board and provide it as a private service. if you don't like the service they provide, you are free to NOT make use of it.
The ONLY way they could get in trouble is if they modified a post to say something libelous - and attributed it to you; or they libeled you personally. But again, neither of these last two situations relate to "Freedom of Speech" as defined in the U.S. Constitution.
Again, CBS and Paramount co-OWN Star Trek. the benefit of that (which they are in fact suing to protect); is that they have the final say as to who is allowed to work on producing Star Trek material; as well as have full say in the final content of that material. You, as a fan, have NO RIGHT to do or make anything Star Trek related - and even if C/P offer guidelines that say "If you follow these and make something Star Trek related we PROBABLY won't take action against you - BUT we retain ALL RIGHTS to do so if we see fit..."<--- Which is what the Guidelines they put forth ultimately do say. They cede fans NOTHING with regard to Star Trek - they are neither a contract nor an implied license.