To last long? It would be wrecked in court. The way to do this for the administration would be to perform an investigation, create a factual record, give Columbia a chance to respond, and then make a decision. That would be hard to attack, even if it was bad faith the entire time.
But as it stands this is just viewpoint discrimination. Without any actual evidence of Columbia committing any wrongdoing, the denial can't be upheld in court. What they are citing -- i.e. whether Columbia or Harvard want to label O7 "violence" or not -- is just a First Amendment protected viewpoint.