Don't agreements like this typically include language to the effect of:
"This agreement is entirely enforceable under the laws of the state of ____, under the jurisdiction of a binding arbitrator chosen by the employer, except for injunctions which are handled by the ____ District Court in ____ County?"
Yes, otherwise it would be trivial to override labor laws via contract. For all they seem like dolts to us, this isn't the administrative class's first barbeque. Attempts to end-run around the law are regularly shot down.
"This agreement is entirely enforceable under the laws of the state of ____, under the jurisdiction of a binding arbitrator chosen by the employer, except for injunctions which are handled by the ____ District Court in ____ County?"