Seriously? I really doubt. GMAT sets one up for the MBA, which, I believe, mandates one to have good analytical skills accompanied with good critical thinking and good hold on written English to start with.
GRE does not focus on critical aspects of the test, and, moreover, focuses too much on unnecessary vocab testing. I am not denying that GRE is a good indicator of "basic" English knowledge and "basic" analytical skills. Nonetheless, for streams such as engineering, science, humanities and so-on, GRE still suffices the need.
However, GMAT, to start-with, is "meant" to be an IQ test, although it is flawed heavily and can be beaten with an average, even perhaps below average, IQ. Nonetheless, GMAT still gives MBA schools a good indicator of the level of the necessary skills needed for business administration in general.
Even if these MBA schools start accepting GRE, I will not be surprised if they are heavily biased towards GMAT. Case in point, they might "subconsciously" rate GMAT over GRE while reviewing ones application. Anyhow, that's my "philosophy"; I am sure Admin Reps know more than me