It should not be rejected outright without at least consulting with actual experts. I know a tiny bit of Standard and Levantine Arabic, but I'm definitely not an expert.
As far as I can tell, it's as eligible as Moroccan and Egyptian Arabic, which we've already approved. And this is true even though Levantive is often mentioned as one of the closest variants to standard Arabic.
There isn't a lot of published written content published in any of the Arabic variants other than Modern Standard Arabic, including Levantine. For the particular case of Levantine, I am aware of a complete translation of The Little Prince. There was a recent political campaign in Israel, with some written material in the local dialect, which is one variety of Levantine. There were also attempts to publish newspapers and books in it in Lebanon, but I know less about that.
It's also widely used in writing on social media. It's informal, but it is a thing nevertheless; if a language is popular on the web in general, it can contribute to its success in a Wikipedia.
So no, it probably shouldn't be rejected outright.
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Amir Elisha Aharoni · אָמִיר אֱלִישָׁע אַהֲרוֹנִי
http://aharoni.wordpress.com“We're living in pieces,
I want to live in peace.” – T. Moore