Can i remove this spoiler and fit a cup

You need to look on the underside of the tailgate and check whether it's just bonded or whether it's bolted on. If it's bolted, unless the cup mountings cover the holes it's a fill and paint, if it's bonded you just have to hope you can warm it and remove it without any damage.
 
New tailgate would be required! I've gust changed a gt tailgate in the last week and there is a big recess under the spoiler.