I have the same van, a 2013 Transit Connect with a Yakima roof rack on it. The bare rack (no solar on it as I use the rack for everything from transporting kayaks to attaching my DIY awning) does knock a mile or two per gallon off your fuel consumption (I get about 22mpg city/26 mpg highway) , but, as previously noted, it's not nearly as important a factor as speed. In 2015, drove from PA to Virginia Beach with two kayaks on the rack and average mpg was 24. However, much of the drive was on roads where the speed limit was 55-65mph.
I got only 22mpg taking I70 across Kansas this summer on my way to Colorado because I was doing 75mph the whole way and often against prevailing winds. I tended to average about 23-24mpg in intermountain West driving as we camped all over CO, WY, MT, and ID this July/August. The weak link is the crappy four speed auto tranny. It sucks, but you already know that. Otherwise, it's an amazingly roomy box for a vehicle with such a small footprint and great turning radius. If you ever head into the mountains, you'll also find the short wheelbase and 7.5 inches of ground clearance will get you into most remote places.