No.
"Inalienable right", like the "right to bear arms", has never meant you get to do anything with it. Free speech doesn't extend to defamation; free expression doesn't extend to murder; freedom of the press doesn't extend to sneaking into the CIA's archives, freedom of movement doesn't apply to jails.
I'm of the opinion that arbitration clauses and non-disparagement agreements of the scope involved in this particular case are unconsionable, because they unreasonably infringe upon such inalienable rights.