After a lot of trial and error, I've managed to get DLC downloaded from Steam working with wine (on linux, rather than OS X, but the principle is the same). Since this thread showed me how to get the base game working, I figured I could return the favor. Doing this takes a little bit of work and may not be for the faint of heart.
1) Install Mono 2.8 for Windows in wine. winetricks has a mono28 target, but it doesn't appear to be working. I had to go to Mono's site, download Mono version 2.8, and install it manually (wine /path/to/mono-2-8-blah.exe). (Why not the newest version, Mono 2.10? There's a bug in it that makes it not work with ck2game.exe. Thankfully, there's a bug report for it that says the issue didn't exist in 2.8, which is why I knew to try it).
2) ck2game.exe will run with Mono 2.8 installed, but it immediately quits because it can't find ck2.exe. (I don't know why, it feels like it should. I think it's a Mono bug.) What you need to do is put the path to ck2.exe in your Windows path. The way to do this is:
2a) "wine regedit" to enter the registry editor in wine
2b) Navigate to HKEY_CURRENT_USER/Environment
2c) Create a String Value (Right click, New -> String Value) called Path if it isn't already there
2d) Have this Path include your path to ck2.exe (mine is: "c:\\windows;c:\\windows\\system;c:\\Program Files\Steam\steamapps\common\crusader kings ii\"
3) Now you should be able to run ck2game.exe. But, you have to run it through Steam for the DLC that you downloaded from Steam to be recognized (makes sense, I guess, but it was disheartening when I ran it manually and it still said I needed to buy the Sword of Islam. I did already!) So, make sure your WINEDEBUG=warn+heap so the regular game runs, fire up Steam, and run Crusader Kings II. The launcher should pop up with all your DLC selected and you should be ready to go.
If not, I may have left something out. I'll try this on a fresh wineprefix tomorrow, but for now, I'm just glad I finally got it working. Hopefully it works for anyone else who wants to play Sword of Islam but needs to use wine to do it. Deus Vult or Allahu Akbar, whichever one you want.