Thule Boxter Box Cargo Carrier ...?

Almost certainly will hit the antenna and also prevent you from opening the hatch all of the way.
You may get some useful info if you call Thule at 800-238-2388.
I just called for info on the Ascent 1600. It's 11" shorter than the Boxster. Thule told me it would probably prevent the hatch from fully opening (not a big deal to me) and it would hit the antenna, bend it, but not damage it. I hear you can get a shark fin antenna to fix the antenna issue.
My biggest concern is the stress you'll put on the feet brackets. They're only 2 feet apart and the long boxes put proportionally more force on the feet. Plus pitch and yaw stability will be compromised. It's similar (but on a smaller scale) to carrying a canoe on the rack. I don't think anyone would drive on the highway without also tying the front and rear of the canoe to the front and rear of the car.
IMHO, the safest compromise is the Ascent 1500--15 cu.ft. and it's only 67" long. Of course you won't fit skis longer than 155 cm in the 1500.
That all said, I want to be able to carry skis and I plan on getting the Ascent 1600 and hoping for the best.

 

Just in case you hadn't checked...
The Atlantis 1600 is 2" shorter than the Ascent (that's good), looks a lot cooler and is available in silver.
The Ascent 1600 is 5 lbs lighter, fits longer skis (186 v. 178 cm), and is about $120 cheaper.
Still not obvious which is better for anyone.

 

I have the Thule Atlantis 1600 (HumblePower.com ~$470 delivered ) on my '08 Prius. The box is mounted full forward, and the antenna just clears.

Hope that helps