Like I said...it will depend on the load you are trying to put on it. If you are trying to run 4,000w of lighting then no. Not unless you duct the air handler entirely to that room. Also depends on the size fo the air handler. Technically it's not even a sealed room. You would need the air handler to be in the room.
You are asking if the setup will work and I am giving you the best guess answer considering you haven't given any specs on the room or its cooling needs and we don't know what size the air handler is.