In his memories general Schwartzkopf mentions that during the 1st Gulf War when Iraq launched Scuds againt Israel, Israelis wanted to retaliate and conduct air raids against Iraqi targets. It caused panic among the coalition leaders, since the Arab allies, especially Saudi Arabia, would never agree to it, not to mention letting Israelis planes into their airspace. I think there was an idea to let Israelis attack unofficially, but it was quickly shot down (pun intended), since there were Arab officers in allies HQ and air control who would have immediately found out about it.
There was also an idea about Israelis getting full access to allied recon and choosing their own targets for allied strikes. It was vetoed (by Schwarzkopf himself, I believe), since allied commanders weren't happy about someone else deciding what their troops were supposed to do.
Anyway, if Israelis are officially or even unofficially in, Arabs are out.