Could the United Arab Republic survive a defeat against Israel?

There are a bunch of threads discussing how plausible and what PODs are needed for the United Arab Republic to survive, but AFAIK none about if the union could've survived a war against Israel, something that seems almost inevitable given the OTL Six-Day War and the Yom Kippur War.

Assuming the worst came to pass and a war took place, how severe a defeat could the union suffer without falling apart? Could an outright armed conflict be avoided?
 
Because the UAR is a very young union comprised of two countries with different structures and interests?
Don’t see the relevance to this as failure of the United Arab Republic was tied to economic policies and centralization. A defeat against Israel is going show the need of sticking it together for the sake of revenge .
 
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