You should ask Tesla before spending the money; but I am almost positive that if your car can't Supercharge, then it can't use the CHAdeMO adapter either. By far the simplest approach is for the CHAdeMO adapter to go through the DC connection used by Superchargers, rather than the AC connection that uses the car's single or twin chargers.
Of course, before spending the money you should also inquire about when the adapter may be available. Some simple features (like text-on-charge-stop) that Tesla promised Roadster owners 2.5 years ago are still not here, so I have some concerns about how long a complicated CHAdeMO adapter will take. I would think the CHAdeMO adapter is important enough (it is likely affecting sales NOW) that they would move on it, but you never know.