I believe copyright law in the U.S. is governed by federal statute and copyright infringement matters would be handled by a federal court.
I also found an unpublished opinion from SCO Group, Inc. v. Novell, Inc., that deals with a similar issue that also makes me think that this software license could work:
> The license in the APA and the TLA does not preclude Novell from pursing its business. Rather, the license merely restricts Novell's ability to use SCO's property and is part of an ongoing relationship between the parties. Therefore, the court finds that there is no restraint on trade and the restrictions are not void under Section 16600.