I have designed and built trailers over the years and here is my take on it.
You won't gain much and you will lose quite a bit.
My TT is very dirty aero wise; vents everywhere, awning, windows with trim sticking out, door frames that stick out, just junk everywhere sticking out (like most).
My car trailer? Pretty clean aero wise. No vents or windows or AC. Nothing, just a clean box. The front has a lean back V front. Both weigh about the same loaded and both are about the same length.
MPG? The car trailer gets 12 MPG and the TT gets 12 MPG. I can't tell any difference in mileage between the two even though the TT is very dirty.
I ran the thing around for years without a box on it. It was just a flatbed car trailer with a race car on it. I would only get a little over 13 MPG with just a car on a flatbed trailer so at the most I would only gain about a MPG.
Sure, you could design it like a tear drop but then again who wants to live or vacation in a tear drop to gain 1 MPG? :W
In 5,000 mile on my vacation I get every year I would only save $100 bucks if diesel was $3 bucks a gallon.
Just stating what I have learned over the years making and towing trailers. :) Anyway have fun with your project.