The UNCITRAL Model Law offers what may be considered a sensible regulation of court measures in connection with international commercial arbitration. Its Article 5 provides:
You should not assume that domestic laws follow the UNCITRAL Model Law.
In conclusion, there is great variation in the domestic legal regulation of court measures within the framework of the New York Convention. You should study that regulation as well as the court practice of the relevant jurisdiction in order to determine the likelihood of courts taking a certain measure.
