Whcih version of WW are you referring to? Post-Crisis (Perez) WW dealt with that in the late 90's with a storyline dealing with the Gods being turned to stone and Zeus was an amnesiac on Earth. Diana joined forces with the Hindu Gods, and she and Zauriel seem to get along well. At the time, DC treated "God" as kind of being an egotistical a$$ who wanted all the power of worship directed to him. Not as plainly put, but pretty much the jist. During that time, DC established that the Gods knew each other existed, they just kinda ignored each other and kept to their own pantheons. Kind of a peace by ignoring kind of deal. Or ignorancve, since most of the gods tend to refuse to believe there are other pantheons out there. In the Nu52, your guess is as good as any.
WW Vol 2 147-150:Godwar
There was the understanding that while you could have other so called gods showing up, the top dog would always be the presence...
And the new gods source somehow seems to be connected to the presence, as Zauriel implied that the two were the same thing!