FlyerTalk Evangelist
Join Date: Nov 2000
Location: Nashville -Past DL Plat, FO, WN-CP, various hotel programs
Programs: DL-MM, AA, SW w/companion,HiltonDiamond, Hyatt PLat, IHF Plat, Miles and Points Seeker
Posts: 11,066
Pretty easy to get an accurate answer - probably faster than calling WN or asking here.
I just went in and tried booking a flight for a full week. No non-stops were available, so I can say for July the answer is no-100% sure. I picked a week later in July since I did not know when you are looking to fly.
Looks like most go/connect through FLL.