Legal Question in Constitutional Law in Virgin Islands

The U.S. Constitution doesn't deal with the internal workings of state and territorial governments. Each of them has its own constitution and its own set of laws that regulate what the governor can and cannot do. The answer to your question may be yes in some states and no in others. The answer might be unclear in some states.

Even where it is clear, the state's courts would likely refuse to intervene in a dispute like this. In part that's due to separation of powers; the courts have very little authority to tell the executive branch how to do its job. It's also because some disputes are more about politics than law; the courts usually let those disputes play out on their own.