Enclosed underbellies do have their pluses and minuses for sure and these have been mentioned in this thread. An enclosed underbelly does improve the aerodynamics but the question here is will that improvement really do much to help your wallet. Those who are quick to dismiss all things as "hype" need to rethink things.
I tow an Airstream and have right at 40K miles on it. The aerodynamics on this thing really do make a difference. After a couple of years we installed a bike rack on the back and I noticed just about a 1 mpg loss in efficiency. It didn't seem to matter if there were bikes attached or not. I used the onboard computer to check and then went to paper and pencil methods and I was down just about one mpg. The rack on the back changed the aerodynamics enough to see the difference at the pump. My underbelly is covered. If I uncovered it I am sure the added turbulence would have an effect.
The issue here is, does the extra turbulence really make that much of a difference to you and is it really all that large? A salesman will push the covered version and make it sound much better than it really is. I suppose this is the hype mentioned earlier. Yes, it is better but how much better? I say, not that much. I like my bike rack and would not think of removing it just to get a bit better towing mileage. This is the same argument I would apply to the underbelly decision. What are the benefits?