Depends on the style of trim you select. Not many premaid ones are less than 1.5" wide. You may have to make your own trim, or cut a chunk out for the vent. I think it would probably look best to make your own trim 1.5" wide.

My basement is getting done and the drywall and texture is up. In my bedroom, there is a long vent below the ceiling and goes in the center at the top of the closet. There's about 1.5 inches from the vent till where it touches the edge of the door frame. The door isn't on but will it be enough room for trim???!