I don't think so, because the JSM doesn't fit into the internal weapon bays of the F-35B. That means they can only be carried externally and as such interferes with the stealth characteristics of the plane.I wonder if this increases the possibility of JSM on the UK F-35s?
The UK is focusing on Spear 3, which can be carried internally and in far larger quantities. We're also developing FC/ASW with the French - JSM would mean a third type of AShM for the Royal Navy to operate and maintain.
Therefore, in my view a JSM purchase would signal the belief that the Royal Navy was likely to tangle with a significant naval power like the PLAN within 12-24 months and immediately needed an AShM for its fighters. Russia doesn't pose the same threat.