Not sure. There's only one way to find out!
I use this to run crysis and 3rd party levels. It can automatically manage them, mods, installations, etc...not to mention letting you run these maps (including original crytek maps) with unlimited weapon carrying so you can hold as many guns as you want!
Edit: It automatically looks for the crysis.exe for crysis not warhead (despite warhead also using crysis.exe to load it's game) so I can't test it using warhead levels. As long as the 3rd party levels are installed correctly though, I'd think that they would work even if you had to do the map load console way of getting into them. Not sure if those levels rely on content from the crysis files though...like textures and models.